Recursive and Explicit Formulas Worksheet

Recursive and Explicit Formulas

Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.

1. A   formula defines each term in a sequence using the previous term(s).

2. An   formula defines each term in a sequence directly by its position.

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

4. The first term of a sequence is often denoted as  .

5. Which of the following is a recursive formula for the sequence 3, 6, 9, 12, ...?

6. For the explicit formula a_n = 2n + 1, what is the 4th term?

7. Write the first 5 terms of the sequence defined by the recursive formula: a_1 = 5, a_n = a_{n-1} + 2

8. Write an explicit formula for the sequence: 10, 20, 30, 40, ...

9. A recursive formula is generally easier to use for finding the 100th term of a sequence than an explicit formula.

10. The sequence defined by a_n = n^2 will always have positive terms.

11. Consider the sequence: 1, 3, 5, 7, ...