Recursive and Explicit Formulas Worksheet

Recursive and Explicit Formulas

Read each question carefully and provide the best answer. Show all your work where applicable.

1. For each sequence, determine if it is arithmetic, geometric, or neither.

2. Complete the recursive formula for each sequence.

a) For the sequence 5, 10, 15, 20, ...: a_1 = 5, a_n = a_(n-1) +  

b) For the sequence 3, 9, 27, 81, ...: a_1 = 3, a_n = a_(n-1) *  

c) For the sequence 100, 50, 25, 12.5, ...: a_1 = 100, a_n = a_(n-1) *  

3. Which of the following is the explicit formula for the arithmetic sequence 8, 11, 14, 17, ...?

4. Write both a recursive and an explicit formula for the sequence: 4, 8, 16, 32, ...

Recursive Formula:

Explicit Formula:

5. Determine if the following statements are True or False.

a) An arithmetic sequence has a common ratio.

b) A geometric sequence can be defined by an explicit formula a_n = a_1 * r^(n-1).