Name: ______

Date: ______

Lesson 2 –Recursive Formulas

A geometric sequencefollows a pattern ofmultiplyinga fixed amount(not zero)times each term to arrive at the following term. The fixed amount multiplied is called thecommon ratio,r,referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple.To find the common ratio, divide the second term by the first term.
Recall: an explicit formula describes the nth term of a sequence using the number n.
Example:
1. What are the first 5 terms of a sequence with an explicit formula ?
What is the initial value? What is the common ratio between terms?
Example:
Recall: a recursive formula states the first term of the sequence and relates subsequent terms to the one before.
2. State the first 4 terms of the sequence:
What is the initial value? What is the common ratio?
3. Is the sequence a geometric sequence? Justify your reasoning.
4. What are the first 5 terms of a sequence with an explicit formula ?
What is the initial value? What is the common ratio between terms?
5. What is the tenth term of the geometric sequence 4, 12, 36, … ?
6. What is the explicit formula for the nth term of the sequence 3, 6, 12, 24, 48, … ?
Write a recursive formula for the sequence 3, 6, 12, 24, 48, … ?
What is the missing terms of the geometric sequence 2, _____ , _____, –54, … ?
A ball is dropped from a height of 8 feet. The ball bounces to 80% of its previous height with eachbounce. How high (to the nearest tenth of a foot) does the ball bounce on the fifth bounce?
The third term of a geometric sequence is 3 and the sixth term is. Find the first term.

Name ______Geometric Sequences

Show all your work

1. A sequence has the following terms:, , , . Which formula

represents the nth term in the sequence?

1) /
2) /
3) /
4) /

2. What is the explicit formula for the nth term of the sequence 6, 18, 54, … ?

3. What is the common ratio of the geometric sequence 2, 8, 32 ?

4. What is the tenth term of the sequence 5, 10, 20, 40, 80, … ?

5. What is the next term of the geometric sequence 1, –5, 25, –125, ______?

6. What are the first 4 terms of a sequence with an explicit formula ?

What is the initial value? What is the common ratio between terms?

7. State the first 5 terms of the sequence:

What is the initial value? What is the common ratio?

8. Is the sequence a geometric sequence? Justify your reasoning.

9. Write a recursive formula for the sequence 1, 3, 9, 27… ?

10. What are the missing terms of the geometric sequence 5, _____ , _____, 320, … ?

11. The fourth term of a geometric sequence is 4 and the seventh term is. Find the first term.