Arithmetic Sequences (9.2)

Arithmetic Sequence: a sequence whose consecutive terms have a common difference

Example:

3, 6, 9, 12, 15, 18, ...

6-3=3, 9-6=3, 12-9=3, etc. The common differnce here is 3

The common difference is represented by d.

The Recursive Formula

Example:

Find the next term in the sequence

3, 6, 9, 12, 15, 18, __

=18, d=3

= 18+3

= 21

The nth Term of an Arithmetic Sequence

Where

Now, since Mr. Wilhelm doesn't like this formula, we can do this:

Start With:

Replace c:

Simplify:

Example:

Find the 10th term.

3, 6, 9, 12, 15, 18, ...

d=3

=3

Formula:

=3(10-1)+3

=30

Sum of Finite Arithmetic Sequence

How it came to be:

Find the sum of all numbers 1-100

=1+2+3+...+98+99+100 Add the first set of numbers to a reverse set of the same numbers

=100+99+98+...3+2+1

=101,101,101,...,101,101,101 All answers are 101 and the sum is doubled

=100(101) Multiply answer by total number of numbers in sequence

=10100/2 Divide by 2 so you get rid of the doubled sum

=5050 ANSWER!

Example:

Find the sume of the sequence:

3, 6, 9, 12, 15, 18

=3

=18

n=6

=63