Recursive and Explicit Formulas Worksheet

Recursive and Explicit Formulas

Read each question carefully and follow the instructions to determine the recursive or explicit formula, or to find specific terms in a sequence.

1. Write the first five terms of the sequence defined by the recursive formula: a₁ = 3, aₙ = aₙ-₁ + 4

2. Write the first five terms of the sequence defined by the explicit formula: aₙ = 2n - 1

3. The recursive formula for the arithmetic sequence 5, 8, 11, 14, ... is a₁ =  , aₙ =  .

4. The recursive formula for the geometric sequence 2, 6, 18, 54, ... is a₁ =  , aₙ =  .

5. The explicit formula for the arithmetic sequence 10, 7, 4, 1, ... is aₙ =  .

6. The explicit formula for the geometric sequence 3, 12, 48, 192, ... is aₙ =  .

7. Which of the following is the 7th term of the sequence defined by a₁ = 5, aₙ = 2aₙ-₁ - 3?

8. An explicit formula allows you to find any term in a sequence without knowing the previous terms.

9. A population of bacteria doubles every hour. If you start with 100 bacteria, write both a recursive and an explicit formula to model the population after 'n' hours. Then, find the population after 5 hours.

Recursive Formula:

Explicit Formula:

Population after 5 hours: