Question

A geometric sequence has the explicit formula a n =13*(-2)^ n-1 What is the recursive formula?

Answer 1

The recursive formula for the given geometric sequence is a1 = 13, and for n ≥ 2, an = -2 * an-1.

Step-by-step explanation:

To find the recursive formula for the geometric sequence given by the explicit formula an = 13*(-2)n-1, we need to express an in terms of the previous term an-1. We know that the ratio between consecutive terms in a geometric sequence is constant. So, we can determine this ratio from the explicit formula by dividing an by an-1:

• Ratio (r) = -2

Here's the recursive formula:

• For n ≥ 2, an = r * an-1
• The first term a1 = 13

Therefore, the recursive formula is:

• a1 = 13
• For n ≥ 2, an = -2 * an-1