1. Coordinate Algebra Day 54
Learning Target:
Students can use the explicit formula to find the nth term of a sequence.

2. Arithmetic Sequences Geometric Sequences Explicit Formula
(Common difference)
Geometric Sequences
(common ratio)
Explicit Formula
Recursive Formula
Explicit Formula
Recursive Formula

3. Arithmetic Sequence
A sequence of terms that have a common difference (d) between them -Subtract terms right to left

4. Geometric Sequence
A sequence of terms that have a common ratio (r) between them -Divide terms right to left

5. Explicit Formula
Formula used to find the nth term of a sequence

6. Explicit Formula for Arithmetic Sequence

7. Explicit Formula for Arithmetic Sequences
a1 + (n-1)d = an
(Allows us to find ANY term in a sequence)
a1= 1st term
n= the number of the term you are looking for
d= common difference
an= the value of the term that you are looking for

8. Explicit Formula for Geometric Sequence

9. Arithmetic or Geometric?
Example:
-22, -15, -8, -1, …
Arithmetic
d = 7

10. Arithmetic or Geometric?
Example:
7, 4, 1, -2, -5
Arithmetic
d = -3

11. Arithmetic or Geometric?
Example:
256, 64, 16, 4, …
Geometric
r = 1/4

12. Arithmetic or Geometric?
Example:
Geometric
r = 2/3

13. Find the common difference, the explicit formula, and the tenth term.
3, 9, 15, 21, …
d = 6
an = 6n – 3
a10 = 57

14. Find the common ratio, the explicit formula, and the seventh term.
3, 1.5, 0.75, 0.375, …

15. The fifth term is 1,792. The constant ratio is 4
The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.

16. Homework
Sequence Practice WS