1. AKS 67 Analyze Arithmetic & Geometric Sequences

2. Vocabulary
In an arithmetic sequence, the difference of consecutive terms is constant. This is called the common difference and is denoted by d. The nth term of an arithmetic sequence with first term a1 and common difference d is given by:
an = a1 + (n-1)d

3. Examples
Tell whether the sequence 4, 8, 16, 22, 32, is arithmetic.
Tell whether the sequence 2, 11, 20, 29, 38, . . is arithmetic.

4. Write a rule for the nth term of the sequence 2, 11, 20, 29, 38,
Write a rule for the nth term of the sequence 2, 11, 20, 29, 38, Then find a15.
This is arithmetic so we use
an = a1 + (n-1)d
Write a rule for the nth term of the sequence 19, 23, 27, 31, 35, Then find a15.

5. Write a rule for the nth term of the arithmetic sequence that has the two given terms.
a20 = 240, a15 = 170

6. Now lets try some examples…
HW: Front side of AKS 67 homework worksheet
Lets #7
HW: Front side of AKS 78 Practice ½ worksheet
Lets #1 & #4

7. Recursive Formula

8. Geometric Sequences:
A geometric sequence has a common ratio (all terms are multiplied by the same number: exponential functions).
The nth term of a geometric sequence with first term a1 and common ratio r is given by:
an = a1r n-1

9. Examples: Tell whether the sequences are geometric.
1. 4, 8, 16, 32, 64, . . .
3, 7, 11, 15, 19, . . .
3/28, 3/7, 12/7, 48/7, . . .

10. Write a rule for the nth term of the sequence 6, 24, 96, 384,
Write a rule for the nth term of the sequence 6, 24, 96, 384, Then find a7.
Write a rule for the nth term of the sequence 7, 14, 28, 56, Then find a9.

11. One term of a geometric sequence is a3 = 16. The common ratio is r = 4
One term of a geometric sequence is a3 = 16. The common ratio is r = 4. Write a rule for the nth term.

12. One term of a geometric sequence is a3 = 16. The common ratio is r = 4
One term of a geometric sequence is a3 = 16. The common ratio is r = 4. Write a rule for the nth term.