1. 13.1 – Finite Sequences and Series
Essential Question: What is the difference between an arithmetic and a geometric sequence?

2. Vocabulary
Sequence – a set of #’s or terms arranged in a particular order.
Arithmetic Sequence – the difference of any 2 consecutive terms is constant.
(common difference, + or – )
When you add the same number to each term.
(NOTE: you can add a negative which looks like subtraction.)

3. Vocab.
Geometric Sequence – the ratio of any 2 consecutive terms is constant.
(common ratio, × or ÷ )
When you multiply each term by the
same number.
(NOTE: you can multiply by a rational number
as well as a whole number.)

4. We use the notation to talk about
the “n”th term.
Formulas for the “n”th term
are as follows:

5. Arithmetic Sequence Common Difference To get the “n”th term
The “n” term
1st term

6. Geometric Sequence The “n” term To get the “n”th term Common Ratio
1st term

7. Example Find a formula for tn and sketch the graph. 1, 4, 7, 10, …
8, 4, 2, 1, …

8. Example
State whether the given sequence is arithmetic, geometric, or neither. Find a formula for tn in terms of n, and evaluate t8. a. b.
c. 15, 11, 7, 3, …

9. Example In a certain sequence, t2 = 2 and t5 = 16.
Find t10 if the sequence is:
arithmetic
geometric

10. Example
Find the # of multiples of 7 between 30 and 300.