Arithmetic Sequence
Aims: To know the nth term rule for an arithmetic Sequence.
Be able to find the nth term of an arithmetic Sequence given sufficient information.
Lesson Outcomes
• Name: Know what an arithmetic sequence is.
• Describe: The nth term rule of an arithmetic sequence and what you need to write it down.
• Explain: How to use other information and/or simultaneous equations to find the nth term rule.
Maths
• 2C p257-258 Q1,2,3,6• Next Lesson: Arithmetic Series.
Summing the terms of arithmetic sequences.
• Bhāskara II: 12th Century Indian Mathematician who wrote Lilavati a text containing some of the earliest work on arithmetic (and geometric) sequences.
An “Arithmetic Sequence”...
• ...is a sequence which increases or decreses by the same value (d) between each term, with a starting term (a). E.g. 3,5,7,9,11...
• The terms are...
• Recursive Definition un+1=un+d u1=a
• nth term ur=a+(n-1)d
un u1 u2 u3 u4 u5
Term a a+d a+2d a+3d a+4d
Finding The nth term
• The nth term rule un=a+(n-1)d
• We need to know a and d so lets find the nth term for these arithmetic sequences...
• 3,7,...,15,...,23• 5,...,...,14...• ...,...,4,...,...,...,16• 5th term 9, 100th term 199
Find the nth term rule
• First Term 0 and Common Difference -9
• un = 0+(n-1)(-9) = 0-(n-1)9 =-9(n-1)
Simultaneous Again!
• An arithmetic sequence has a third term that is three times the first and double the second.
• If the common difference is 8 find the nth term rule.
Trickier Simultaneous
• The first three terms of an arithmetic progression are…
• t, 2t + 2 and 4t – 2 respectively.
• Find the value of t and hence write down the nth term rule.