Geometric Sequence Problem

Question

Given two terms in a geometric sequence find the term named in the problem & the explicit formula:

1. a₆ = -128 and a₃ = -16

find a₁₂

Answer 1

a_n = a₁ . r^n-1

Set up 2 equations a₆ and a₃ using the explicit formula above.

a6 = a₁ . r^6-1 = -128

a3 = a₁ . r^3-1 = -16

Divide equation 1 by equation 2 and solve for r.

r³ = 8

r = 2

plug r value back in on of the equation to solve for a₁