Recursive Formulas Worksheet

Recursive Formulas

Read each question carefully and follow the instructions to determine terms in sequences or write recursive formulas.

1. Find the first five terms of the sequence defined by a₁ = 3 and aₙ = aₙ₋₁ + 4 for n > 1.

2. Find the first four terms of the sequence defined by a₁ = 10 and aₙ = 2 * aₙ₋₁ - 5 for n > 1.

3. A sequence starts with 5, 10, 15, 20, ... The recursive formula is a₁ =   and aₙ =  .

4. A sequence starts with 2, 6, 18, 54, ... The recursive formula is a₁ =   and aₙ =  .

5. Which recursive formula describes the sequence: 7, 10, 13, 16, ...?

6. Given the recursive formula a₁ = 20 and aₙ = aₙ₋₁ / 2, what is the third term (a₃) of the sequence?

7. A plant grows 2 cm each week. If it starts at 5 cm tall, write a recursive formula for its height after 'n' weeks.