Sequences and Series. Find the pattern for each of the following. 1. 5, 8, 11, 14, …. 2. 16, 8, 4, 2, … 3. 1, 4, 9, 16, 25, … 4. 1, 1, 2, 3, 5, 8, 13,

Sequences and Series

Find the pattern for each of the following.

1. 5, 8, 11, 14, ….

2. 16, 8, 4, 2, …

3. 1, 4, 9, 16, 25, …

4. 1, 1, 2, 3, 5, 8, 13, 21, ….

Sequences

A sequence is a list of numbers that are in a particular order.

To create the numbers of a sequence is to generate the sequence. Most often the sequence is generated by a particular generating function.

The generating function for sequences are usually denoted as an = _________.

Examples of generating functions

an = 4 + 3(n – 1)

Each number in a sequence is a term of the sequence

a5 indicates the 5th term of sequence a.t11 indicates the 11th term of sequence t.

Term number 1 is the first term of the sequence, this means to find it you would plug 1 into the variable of the generating function.

Find the first 5 terms of an = 3n2 – n

Now find the 25th term of the sequence.

Try These:

1. Find the first 4 terms of tn = n2 - 10.

2. Find the first 4 terms of an = -2n + 3

3. Find the 10th term of bn = .5n3 – 1

4. Find the 8th term of 2 1

3n

na

n

Fortunately, your graphing calculator will help you out.Here is a screen shot of a TI-Nspire

You can just type in seq(generating function, variable, start,

end)

Or find it by pressing menu, 6, 4, 5

Try These.

Find the first six terms of the following sequences.

1. an = 2n+ 3

2. tn = (n)2 – 4

3. bn = n – 2n

One thing that we often want to do is sum up a sequence. When you sum up the terms of a sequence you are dealing with a series rather than a sequence.

Sn indicates the sum of the first n terms of the series.

S12 means to add up the first 12 terms of the series.

S100 means to add up the first 100 terms of the series.

We usually use sigma notation to represent series.

Sigma Notation

Σ is used to express a series and its sum.

10

1

3 4n

n

Find the following sums

1.

2.

Find the following sums

4

1

2 3n

n

Once again, thank goodness for our calculators, here is another screen shot.

You can just type in sum and seq, this is the easy option. Or sum is found by pressing Menu, 6, 3, 5 and seq by pressing Menu, 6, 4, 5

Or use the |□|{ key and find Σ

Find the sum of the following series. Use your calculator.

1.

2.

3.