Recursive and Explicit Formulas Worksheet

Recursive and Explicit Formulas

Read each question carefully and provide your answer in the space provided. Show all your work for full credit.

1. A   formula defines each term of a sequence using preceding terms.

2. An   formula defines any term of a sequence based on its position in the sequence.

3. An arithmetic sequence has a   difference between consecutive terms.

4. A geometric sequence has a   ratio between consecutive terms.

For each sequence, identify if it is arithmetic, geometric, or neither. Explain your reasoning.

5. 2, 5, 8, 11, ...

6. 3, 6, 12, 24, ...

7. 1, 4, 9, 16, ...

8. Which recursive formula represents the sequence 5, 10, 15, 20, ...?

9. Write an explicit formula for the arithmetic sequence: 4, 7, 10, 13, ...

10. Write an explicit formula for the geometric sequence: 2, 8, 32, 128, ...

11. The sequence 1, 1, 2, 3, 5, 8, ... (Fibonacci sequence) can be represented by a simple explicit formula.

12. Given the recursive formula a_1 = 3, a_n = a_(n-1) + 2, find the first 5 terms of the sequence.

13. Given the explicit formula a_n = 3n - 1, find the 10th term of the sequence.