1. Arithmetic Sequences

2. Arithmetic Sequence
An arithmetic sequence is defined as a sequence in which there is a common difference between consecutive terms.
Common Difference = 5

3. Is the given sequence arithmetic? If so, identify the common difference.
2, 4, 8, 16, …
4, 6, 12, 18, 24, …
2, 5, 7, 12, …
48, 45, 42, 39, …

4. Arithmetic Sequence Formula
The 1st number in the sequence.
The common difference.
an = a1 + (n – 1) • d
The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5.
The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence.

5. Example 1:
an = a1 + (n – 1) • d
Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term.

6. Example 3:
an = a1 + (n – 1) • d
Given the sequence 81, 80.5, 80, 79.5, 79,…, find the 9th term.

7. Example 4:
an = a1 + (n – 1) • d
Given the sequence 79, 75, 71, 67, 63,…, find the term number that is -169.

8. Example 5:
an = a1 + (n – 1) • d
Suppose you are saving up for a new gaming system. You have 100 dollars this year, and you plan to add 33 dollars each of the following years. How much money will you have in 7 years?

9. Geometric Sequences

10. Geometric Sequences
An geometric sequence is defined as a sequence in which there is a common ratio between consecutive terms.
Common Ratio = 2

11. Is the given sequence geometric? If so, identify the common ratio.
5, 15, 45, 135, …
15, 30, 45, 60, …
6, -24, 96, -384, …
7, 0.7, 0.07, 0.007, …
10, 4, 1.6, 0.64, …

12. an = a1 • r (n-1) Geometric Sequence Formula The common ratio.
The 1st number in the sequence.
The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5.
an = a1 • r (n-1)
The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence.
The common ratio.

13. Example 1:
an = a1 • r (n-1)
Given the sequence 4, 28, 196, 1372, 9604,…, find the 14th term.

14. Example 2:
an = a1 • r (n-1)
Given the sequence -2, 6, -18, 54, -162,…, find the 17th term.

15. Example 3:
an = a1 • r (n-1)
Given the sequence 100, 83, 68.89, ,…, find the 9th term.

16. Example 5:
an = a1 • r (n-1)
Suppose you want a reduced copy of a photograph. The actual length of the photograph is 10 in. The smallest size the copier can make is 64% of the original. Find the length of the photograph after five reductions.