1. Homework Check

2. How do I find the sum & terms of geometric sequences and series?
Essential Question: What is a sequence and how do I find its terms and sums?
How do I find the sum & terms of geometric sequences and series?

3. Geometric Sequence
Geometric Sequence– a sequence whose consecutive terms have a common ratio.
You multiply to get the next term.

4. Geometric Sequence
A sequence is geometric if the ratios of consecutive terms are the same.
The number r is the common ratio.

5. Formula for a Geometric Sequence
an = a1r n – 1

6. Ex. 1 2, 4, 8, 16, …, formula?, … 12, 36, 108, 324, …, formula?, …
Are these geometric? If so, find the formula.
2, 4, 8, 16, …, formula?, …
an = 2(2)n – 1
12, 36, 108, 324, …, formula?, …
an = 12(3)n – 1
an = (-1/3)(-1/3) n – 1
1, 4, 9, 16, …, formula? , …
Not geometric, but what is the formula?

7. Ex. 2
Write the first five terms of the geometric sequence whose first term is a1 = 9 and r = (1/3).
an = a1rn – 1

8. Ex. 3
Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05
an = a1rn – 1
a15 = (20)(1.05)15 – 1
a15 =

9. Ex. 4 Find a formula for the nth term. 5, 15, 45, … an = a1rn – 1
an = 5(3)n – 1
What is the 9th term?
an = 5(3)n – 1
a9 = 5(3)8
a9 = 32805

10. Ex. 5 Find the first 3 terms an = 36(3)n – 3 a1 = 36(3)1-3
4, 12, 36

11. Ex. 6
The fourth term of a geometric sequence is 8, and the 7th term is 1. Find the geometric rule.
an = a1rn-1
a4 = 8
a7 = a4r7-4
a7 = 1

12. Sum of a finite geometric series

13. Ex. 7
Find the sum:
= 1.714

14. Find the value of n for the geometric series
Ex. 8
Find the value of n for the geometric series
Take the log base 6 of both sides or use the definition of a log to solve for n

15. What are your questions?

16. Homework: WS #1-39 odd