Question

What is the recursive formula of the geometric sequence?

A) an = (2) * (1/2)^n - 1 for n ≥ 1
B) a1 = 1/2; an = an - 1 * (3/2) for n ≥ 2
C) a1 = 1/2; an = an - 1 * (2) for n ≥ 2
D) an = (1/2) * (1/2)^n - 1 for n ≥ 1

Answer 1

The recursive formula for the geometric sequence is a1 = 1/2; an = an - 1 * (3/2) for n ≥ 2.

Step-by-step explanation:

The recursive formula of a geometric sequence is used to find any term in the sequence based on the previous term. The correct recursive formula for the given options is option B) a1 = 1/2; an = an - 1 * (3/2) for n ≥ 2.

This means that the first term (a1) is 1/2, and each subsequent term (an) is found by multiplying the previous term by (3/2). For example, a2 = a1 * (3/2), a3 = a2 * (3/2), and so on. This recursive formula allows you to find any term in the geometric sequence.