Recursive Formulas Worksheet

Recursive Formulas

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

1. A recursive formula defines each term of a sequence using one or more of the   terms.

2. In a recursive formula, you need to know the first term, also called the   term, to find the subsequent terms.

3. For the sequence where each term is 3 more than the previous term, and the first term is 5, the second term is  .

1. Given the recursive formula a_n = a_(n-1) + 4 and a_1 = 2, write out the first 5 terms of the sequence.

2. Write a recursive formula for the sequence: 10, 20, 30, 40, ...

1. Which of the following is the third term of a sequence defined by a_n = 2 * a_(n-1) and a_1 = 3?

2. A sequence starts with 1 and each subsequent term is found by adding 5 to the previous term. What is the recursive formula for this sequence?

1. A recursive formula always requires the first term to be stated.

2. The sequence 2, 4, 6, 8, ... can be represented by the recursive formula a_n = a_(n-1) + 2, with a_1 = 2.

A plant grows 3 cm each week. If it starts at a height of 5 cm, write a recursive formula to represent its height after 'n' weeks. Then, find its height after 4 weeks.