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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 1 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 2 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Problem: ,......3,2,1 nnnAre in A.P. find ., .138 nandttt
112 =+= nnd)1(8178 +=+= ndat
What do you call this
sequence?
What is A.P?
What do you call the fixed
number?
By which, common difference
is denoted?In the A.P, 3, 7, 11, 15..
what is a and d.
What is formula for general
term in A.P?
If3
4=a and d=2 find 7t
and nt ?
Find 7t .
Find .nt
What is given A.P?
What is first term?
Find common difference d?
Find .8t
A.P
Arithmetic Progression is a sequence in which
each term, except the first is obtained by adding a
fixed number to the term immediately preceedingit
Common difference
d
a=3; d=2
dna )1( +
3
4=a and d=2
3
3212
3
426
3
4
)17(
7
7
=+
=+
=
+=
t
dat
3106
3102
3
4222)1(
3
4
==
=+=
nn
nntn
,......3,2,1 nnn1n
112 =+= nnd981)1(8178 ==+=+= nnndat
13
121)1(1211213
=
=+=+=
n
nndat
0)1)(1()1()1( =+=+= nndnatn
Analyti
cal
method
What is
nth term
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Recapitulation: 1.What is the general form of nth term in AP?
2. Find 100t
Behavioral changes: Students find the required terms in A.P.
Assignment: exercise (1) problems 1 to 22.
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 3. APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
C l i / / b Aid / i
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Problem: The 8th term of an A.P is
17 and the 19th term is 39. Find 25th
term.
178 =t and 3919 =t
?25 =t
dat 78 += =17..(1)
39189 =+= dat (2)
211
22
2211)1()2(
==
=
d
d
31417
17)2(7
==
=+
a
a
51483)2(243
2425
=+=+=
+= dat
Problem:2: If 7 times of the 7thterm of AP is equal to 11times of
the 11th term. Show that 18th term is
zero.
dat 67 +=
............427)6(77 7 dadat +=+=
What is the nth term in A.P?
Find the common difference
in the A.P ,........3
5,
3
4,
xxx
What is the next term in this?
What is given?
What is required?
Write 8th term in A.P?
Write 19th term in A.P?
Solve (1) and (2) and find a, d
Find .25t
What is to be proved?
Write PinAt .7 ?
Find 7 times of 7th term.
Write 11th term in A.P?
dnatn )1( +=
Find33
34
3
4 xxxx
xd =
==
36
335 xxx =+
178 =t and 3919 =t
?25 =t
dat 78 += =17..(1)
39189 =+= dat (2)
211
222211)1()2(
==
=
d
d
31417
17)2(7
==
=+
a
a
51483)2(243
2425
=+=+=+= dat
18th term is zero
dat 67 +=
)1......(..........427)6(77 7 dadat +=+=
dat 1011 +=
)2........(11011)10(111111
dadat +=+=
Analyti
cal
method
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Recapitulation: 1.If ba btat = ,then what is bat + ?
Behavioral changes: students find required term in A.P.
Studnets understands that m times of mth tem is equal to ntimes of nth term the (m+n)th term is zero.
Assignment: exercise 1 problems No.25 to 30.
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 4 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
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Recapitulation: 1. what is the sum of n terms in A.P?2. If first term is a and last term is l then what is the sum of n terms in A.P?
Behavioral changes: 1.Students understanding the gauss method of summation of A.P?
2. Students recall the formula for nth term in A.P?
3. Students find the sum of terms (number of terms given) in A.P.
Assignment: Exercise problems 1 to 15.
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 5 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/expe
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments to
be done
/demonstr
ations etc.
method Evaluation
By teacher By Pupil
Problem1: Find the sum of 16, 11,
6 ,.. to 23 terms.
Problem: if 20,10;3
2=== nld
Find sum of 20 terms
What is the n th term in an A.P?
What is the formula for sum of n
terms in A.P?
If an AP has n terms and the first and
last terms are a and l then what is?nS
The terms are in which progression?
What do you find?
What is the first term?
Find common differenced?
What is n?
Find ?23S
What is given required in this
problem?
What is the formula for finding sum of
dnatn )1( +=
( )dnan
Sn )1(22
+=
)(2
lan
Sn +=
A.P
23S
16=a
51611 ==d
n=23
( ) )1(22
dnan
Sn +=
( ))5)(123(1622
2323 +=S
=
( ) 392378223)11032(
223 ==
=-897
20,10;3
2=== nld
)(2
lan
Sn +=
dnal )1( +=
Deductive
method
?23S
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Content analysis/concepts/sub Aids/experiments
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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Arithmetic mean: when three
quantities are in A.P, the middle
term is called arithmetic mean ofthe other two.
Arithmetic means:
Problem: Insert 5 arithmetic means
between 4 and 22.
Give an example for A.P?
Take any three terms which
are in A.P?
What is the average of 7 and15?
What do you call 11?
If a, b c are in A.P, what do
you call b?
If a, b, c are in AP, then their
common difference
Find the A.M of a, b.
Observe this A.P. how many
numbers lies between 2 and17? What are they?
What do you call 5,8,11,14,17
between 2 and 17.
Let take any 5 arithmetic
means between 4 , 22.
22,,,,,4 ,54321 aaaaa Are in
which progression?
How many terms are there?
Wh t i 7th
t ?
3, 7, 11, 15..
7,11,15
112157 =+
-------
Arithmetic mean of a and c
2
2
ca
b
acb
bcabd
+=
+=
==
2
.,,
baA
PAbAa
+=
4.
5,8,11,14,17
Arithmetic means
22,,,,,4 ,54321 aaaaa
A.P
7
22
67 += dat
2,5,8,11,14,17
Analyti
cal
method
What is
A.M of x
and y?
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Recapitulation: 1.what is arithmetic mean?2. What is the A.M of a and b?
3. If a, b, c are in A.P, is b?
Behavioral changes: 1.students understands concept of A.M.
2. Students find the A.M of given two numbers.
3. Students insert the Arithmetic means between two given numbers.
Assignment: 1.Exercise -2; Problems 19 & 20.
2. What is the A.M of a + b and a-b?3. If n A.Ms are in between a and b. then find common differenced.
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 6 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/experiments
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y pconcepts Activities indicating behavioral/learning out comes
pto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Arithmetic mean: when three
quantities are in A.P, the middle
term is called arithmetic mean ofthe other two.
Arithmetic means:
Problem: Insert 5 arithmetic means
between 4 and 22.
Give an example for A.P?
Take any three terms which
are in A.P?
What is the average of 7 and15?
What do you call 11?
If a, b c are in A.P, what do
you call b?
If a, b, c are in AP, then their
common difference
Find the A.M of a, b.
Observe this A.P. how many
numbers lies between 2 and17? What are they?
What do you call 5,8,11,14,17
between 2 and 17.
Let take any 5 arithmetic
means between 4 , 22.
22,,,,,4 ,54321 aaaaa Are in
which progression?
How many terms are there?
Wh i 7th
?
3, 7, 11, 15..
7,11,15
112157 =+
-------
Arithmetic mean of a and c
2
2
ca
b
acb
bcabd
+=
+=
==
2
.,,
baA
PAbAa
+=
4.
5,8,11,14,17
Arithmetic means
22,,,,,4 ,54321 aaaaa
A.P
7
22
67 += dat
2,5,8,11,14,17
Analyti
cal
method
What is
A.M of x
and y?
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Recapitulation: 1.what is arithmetic mean?2. What is the A.M of a and b?
3. If a, b, c are in A.P, is b?
Behavioral changes: 1.students understands concept of A.M.
2. Students find the A.M of given two numbers.
3. Students insert the Arithmetic means between two given numbers.
Assignment: 1.Exercise -2; Problems 19 & 20.
2. What is the A.M of a + b and a-b?3. If n A.Ms are in between a and b. then find common differenced.
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 7 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub concepts Aids/experiments
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y p pActivities indicating behavioral/learning out comes
pto be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Now we find sum of squares of first
n natural numbers:
Sum of squares of first n natural
numbers ++=6
)12)(1(2 nnnn
26
)12)()(1()12)(1(
x
xxxxxx
=
++
2
2
2
)32)(1)(2()12()1(
1
.......................................
3.65.3.27.4.33
2.63.2.15.3.22
1.61.1.03.2.11
nx
nnnnnn
nx
x
x
x
=
=
==
==
==
What is the general term in
A.P?
What is the sum of n terms in
A.P?
Write first n natural numbers
Are these terms are in A.P?
What is a and d?
Find sum of n naturalnumbers?
Sum of first natural numbers
are denoted byn .
Give any algebraic identity?
Why do you call this is an
identity?
What are the squares of first
n natural numbers?
What is their sum?
Substitute for x=1, 2, 3n ,
add and observe then
Add all terms and simplify.
dna )1( +
)(
2
lan
+
1,2,3,4,5,6..n
yes
a=1 d=1
)1(2
nn
Sn +=
= n )1(2
nn+ =
2
)1( +nn
222 2)( bababa ++=+
For all possible values of a and b the above
statement is true.
2222,........,3,2,1 n
-----
2
2
2
2
.6)12()1()12)(1(
)32)(1)(2()12()1(
1
.......................................
3.65.3.27.4.33
2.63.2.15.3.22
1.61.1.03.2.11
nnnnnnn
nx
nnnnnn
nx
x
x
x
=++
=
=
==
==
==
)...321(6)12)(1( 2222 nnnn ++++=++
2
Analyti
cal
method
10 ?
Give an
example
of
identity?
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Recapitulation: 1) =?n
2) =?2
n
3) =?3
n
Behavioral changes: Students understanding to find the formulas of ,n ,2n 3n .
Students observe ( )23 = nn
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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 8 APSWRSCHOOL/JC, PVP
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub Aids/experiments
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concepts Activities indicating behavioral/learning out comes to be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
Problem: Find the sum of n terms
of the series 1.3+3.5+5.7+.+nterms
What is the sum of 1+1+1+.
+1(20terms)
What is 1+1+1+.+1
(n times)
What isn ?
what is ?2
n
what is ?3
n
What is required to find?
If nth term in the series is nt
Then what is sum of n terms?
For finding the sum of n terms
in the series what do you find?
What is the given series?
How is every term in the
series?
What are the first factors inthe series?
Take in the same order; the
terms are in which
progression?
Find n the term?
What are the second factors in
20
nn =1
n =2
)1( +nn
++=6
)12)(1(2 nnnn
+=4
)1( 223 nnn
Sum of n terms
nt
n the term in the series
1.3+3.5+5.7+.
Every term has factors
1, 3, 5
A.P
a=1,d=3-1=2
12
2)1(1)1(
=
+=+=
n
ndnatn
3, 5, 7,
Analyti
cal
method
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Recapitulation: How do you find the sum of n terms in the given series?
Behavioral changes: Students find the sum of n terms in given series.
Student can solve various applicative problems.
Assignment: exercise 3.
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Recapitulation: 1.what is relation between ?, 23 nandnn
Behavioral changes: Students understand the relation between ?, 23 nandnn
Assignment: find the sum of n terms of nterms+++++++ .......)321()21(1
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PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 10 APSWRSCHOOL/JC, KOPPERLA
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
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concepts Activities indicating behavioral/learning out comes to be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
We observe that each term, exceptthe first, is obtained by multiplying
the term immediately preceding it
by a fixed number, of course non-
zero. Such sequences are called
geometric Progressions or briefly
G.P.
Geometric progression:
G.P is series in which the ratio of
each term except first term to the
preceding term is a constant; this
constant is called common ratio (r).
If the first term is a and the
common ratio (r), then the series
takes the form
..........,,, 32 ararara
The thn term or General Term of
a G.P:
Observe the following series?
In each of this sequence, wenote that each term, except the
first, Progresses in a definite
manner.
In the second example first
term ?1t
In the second example second
term ?2t
In the second example 3rd term?3t
Do you know name of the
series?
In G.P what is the ratio of
each term to the preceding
term?
What is called the constant?
Write general terms in the
G.P?
What is the ratio of first twoterms?
What is the general ratio?
Write a series of G.P?
In the series what is the first
term?
n2...,.........32,16,8,4,2
,3,3,3,3 432
n)01.0(000001.0,0001.0,01.0
23121 2,2,2 ttttt === and so on.
3
2333 =
32 333 =
-
Is constant. rt
t=
2
1
Common ratio
..........,,,32
ararara
a
arr
t
t==
2
1
r
t
t
r
r =
1
..........,,,32
ararara
a
ar
111
== arat
122
== arart
1323
== arart
Analyti
cal
method
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Recapitulation: Define G.P?Given an example of G.P?
What is the thn term of G.P?
Behavioral changes: Student understands the definition G.P
Student gives the examples of G.P. students identifying the G.P.
Students solve the problems.
Assignment: solve exercise 4 problems on page No.139.
PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 11 APSWRSCHOOL/JC, KOPPERLADate and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
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concepts Activities indicating behavioral/learning out comes to be done
/demonstrations
etc. method Evaluation
By teacher By Pupil
If a, b, c are in G.P. b is said to be the
geometric mean between a and c.
a ,b ,c are in G.P b
c
a
b
=acbacb ==
2 (a
and c are +ve)
The geometric mean of p and q ispq
Problem:
Inset 5 geometric mean between
.2433
1and
3
1, 543,21
,,, ggggg ,243 PG.
5 + 2 = 7
3
1=a
24367 == art
3
37292433
1 666
=
===
r
rr
3
11 == at
Define arithmetic mean?
If a, b, c is in G.P. then what is
called b?
If a, b, c is in G.P. Find the
common ratios?
If and c are positive find b?
What is the geometric mean of
6 and 24?
Let take any 5 geometric
means?
If insert between .2433
1and
all the numbers are in which
progression?
How many numbers are there?
What is the first term?
What is the last (7th) term?
Replace3
1=a , we have
Find the eometric means?
If a, b, c are in A.P then b is called arithmetic
mean of a and c.
Geometric mean
=rb
c
a
b =
acbacb ==2
12144246 ==
543,21,,, ggggg
3
1, 543,21 ,,, ggggg ,243 PG.
5 + 2 = 7
3
1=a
2436
7 == art
3
37292433
1 666
=
===
r
rr
133
1
3
1
12
1
====
==
argt
at
Analyti
cal
method
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Recapitulation: Define geometric mean of three numbers?
What is the geometric mean of a and b?
What is the value of ( ) ?)( 22 yxyx ++
Behavioral changes: Students understanding the concept of geometrical mean.
Student finds the geometric means between any two numbers.
Students find the numbers when A.M and G.M is given?
Assignment: solve the exercise problems page No.145
PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAO
LESSON PLAN FORMAT PGT MATHS
PERIOD: 12 APSWRSCHOOL/JC, KOPPERLA
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments to be
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concepts Activities indicating behavioral/learning out comes ments to be
done
/demonstrat
ions etc.
method Evaluation
By teacher By Pupil
The sum of the first n terms
of a G.P.:
32 ++++=n arararaS
n
arararrS +++=32
)1( n
n
ra
ara
=
=
r
raS
n
n
=1
)1((r
= rr
raS
n
n
Problem:Find sum of 8 terms in the
geometric progression 3, 6, 12,
24..?
What is the sum of n terms?
What is thn term in G.P?
What is the sum of n terms in
G.P?
Let us take first term of a G.P.
as
What is common ratio?
Let us we write sum of n
terms
Find nrS =
Find nn rSS ?
)1( rSn
Find nS ?
What is the last term in G.P?
Using l rewrite the nS ?
Write given geometricprogression?
( )dnan
Sn )1(22
+=
1=
nn art
-----
a
r
132 +++++=
n
n ararararaS
nn ararararrS ++++=
32
)1( n
n
ra
ara
==
r
raS
n
n
=1
)1((r
= r
r
raS
n
n
1=
narl
1
=r
alrSn
3, 6, 12, 24..?
Analyti
cal
method
What is
the sum
o0f nterms in
G.P?
i l i h i h f l f f i G ?
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Recapitulation: What is the formula of sum of n terms in G.P?
Behavioral changes: Students understanding the deduction of the formula of sum of n terms in G.P.
Students solve the problems related to above formula.
Assignment: solve exercise problems page No.170.
PROGRESSIONS APSWREISOCIETY J Vi
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PROGRESSIONS APSWREISOCIETY J.Visweswara raoLESSON PLAN FORMAT PGT MATHS
PERIOD: 13 APSWRSCHOOL/JC, kopperla
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
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p g g
/demonstrations
etc. method Evaluation
By teacher By Pupil
Problem:
Calculate ( )=
+11
1
32k
k?
Problem:2
What is the formula of sum of
n terms in G.P?
What is given?
Expand?
Find the value
=11
1
2k
?
Find the Value=
11
1
3k
k?
The terms are in which
progression?
Find 11S ?
( )=
+11
1
32k
k
r
raS
n
n
=1
)1((r
= rr
raS
n
n
( )=
+11
1
32k
k
==
+11
1
11
1
32k
k
k
=2+2+2+----+2=22
113213333 +++=
Geometric progression
13
)13(3
1
)1(
133
3,3
11
2
=
=
>===
r
raS
ra
n
n
2
)13(3 1111
=S
=22+2
)13(3 11
3,21, ggg
,m 3,21, ggg ,n
Analyti
cal
method
n
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Recapitulation: what is the value of ?11
=
n
n
If 3,21, ggg are three geometric means between m and n. what is the relation between them?
Behavioral changes: student solves different type of applicative problems using geometric progression concepts.
Assignment: solve exercise 5 problems page No.145.
PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAO
LESSON PLAN FORMAT PGT MATHS
PERIOD: 14 APSWRSCHOOL/JC, KOPPERLA
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experimentsto be done
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p g g
/demonstrations
etc. method Evaluation
By teacher By Pupil
Infinite Geometric progressions:
Let us consider the G.P
,......9
4,
3
2,1 find the sum of
n terms of this G.P is?
What happens if the number
of terms n becomes larger and
larger.
If n=1 find the valuen
3
2
If n=5 find the value
n
3
2
If n=10 find the valuen
3
2
If n=40 find the valuen
3
2
We see that as n becomes
Larger and largern
3
2
becomes smaller and smaller.
It approaches zero.
How to write?
What is formula of sum of nterms is r
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Recapitulation: What is the sum of infinite terms in G.P?
Behavioral changes: students understanding infinite geometric progression.
Students converting a recurring decimal number into rational number with the help of sum of infinite series.
Assignment: solve exercise problems page No.148.
PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAO
LESSON PLAN FORMAT PGT MATHS
PERIOD: 15 APSWRSCHOOL/JC, KOPPERLADate and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/sub conceptsActivities indicating behavioral/learning out comes
Aids/experiments to be
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done
/demonstratio
ns etc.
method Evaluation
By teacher By Pupil
HORMONIC PROGRESSION(H.P):
A progression is said to be Harmonic
Progression, if the reciprocals of these
terms form an arithmetic progression.
The nth term of H.P:
dnatn
)1(
1
+=
There is no concise general formula for
the sum of n terms in H.P.
PROBLEM: in a harmonic progression
the 4th term is9
1and 13th term is
27
1.
Write the harmonic progression.
Consider the sequence
,......12
1,
9
1,
6
1,
3
1what are the
reciprocals of these terms?
3, 6,9,12 these term are belongs to
which progression?
What do you call the progression?
,......12
1,
9
1,
6
1,
3
1is a harmonic
progression why?
Take general terms in A.P?
What is the nth term in A.P?
What is its reciprocal?
nth term in harmonic progression
Let us take a harmonic progression
What is the 4th term?
They are 3,6,9,12 respectively
They are in A.P
------
Their reciprocals are in A.P
3, 6,9,12 PA.
PareinAdadaa .,.........2,, ++dna )1( +
dna )1(
1
+
=dna )1(
1
+
,......3
1,
2
1,
1,
1
dadadaa +++
)1(93
9
1
3
1
=+
=+
da
da
Analyti
cal
method
What is
the nth
term in
H.P.?
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Recapitulation: Define harmonic progression?
What is the nth term in H.P?
If x, y are in H.P. what is the harmonic mean between x and y?
What is the relation between A, G, H?
Behavioral changes: Students recall A.P and understanding harmonic progression.
Students find the required term in H.P.
Students solve problems.
Assignment: Solve exercise problems page No.151
PROGRESSIONS APSWREISOCIETY J VISWESWARA RAO
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PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAOLESSON PLAN FORMAT PGT MATHS
PERIOD: 16 APSWRSCHOOL/JC, KOPPERLA
Date and Time: class: X Subject: Maths Medium: English
Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes
Aids/experiments to be
d
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done
/demonstrat
ions etc.
method Evaluation
By teacher By Pupil
Insert 4 harmonic means between
42
1
12
1and
Problem:
If )(),(),( baandaccb +++ are
in H.P.show that 2221
,1
,1
cba
will also be in H.P.
What is the harmonic mean of
a and b?
Let take 4 harmonic means
Insert these harmonic means
How many terms are there inH.P?
What is the 6th term?
What is the first term?
Find d?
Find harmonic means.
What is given?
What is the harmonic mean of
a and b?
Find harmonic mean of given
ba
abH
+=
2
4321
1
,
1
,
1
,
1
hhhh
12
1,
4321
1,
1,
1,
1
hhhh,42
1
6 terms
)1(425
42
1
5
1
=+
=+
da
da
1212
11== a
a
65
30
3012425
42512
425
==
==
=+
=+
d
d
d
da
36
11,
30
11,
24
11,
18
11
4321
====hhhh
PHbaandaccb .)(),(),( +++
ba
abH
+=
2
2)(2)2)((
))((2
bbccabaacbac
bacb
bacbac
+++=+++
+++
++=+
Analyti
cal
method
Recapitulation: What is the relation between A.M, G.M, and H.M of two given numbers?
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Recapitulation: What is the relation between A.M, G.M, and H.M of two given numbers?
If 2222 cab += then 222 ,, cba are in which progression?
Behavioral changes: Students understanding the relationship between A.M, G.M and H.M
Students solve application of harmonic progression problems.
Assignment: solve exercise 7 page No.151.
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