Recursive and Explicit Formulas Worksheet

Recursive and Explicit Formulas

Read each question carefully and follow the instructions to determine the recursive or explicit formula for the given sequences.

1. A   formula defines each term in a sequence based on the preceding term(s).

2. An   formula defines each term in a sequence directly as a function of its position.

3. In the sequence 2, 4, 6, 8, ..., the common   is 2.

4. Which of the following is an explicit formula for the sequence 3, 6, 9, 12, ...?

5. What is the next term in the sequence defined by a_1 = 5, a_n = a_{n-1} + 2?

6. Write the first 4 terms of the sequence given by the recursive formula: a_1 = 3, a_n = a_{n-1} + 5.

7. Write an explicit formula for the arithmetic sequence: 7, 10, 13, 16, ...

8. Write a recursive formula for the geometric sequence: 2, 4, 8, 16, ...

9. An explicit formula is always preferred over a recursive formula.

10. The sequence 1, 1, 2, 3, 5, ... is defined by a recursive formula.