Algebra question

Question

The differences between the terms of the geometric sequence are known: '[a₂-a₁=-6,a₃-a₂=12' Find the sum of the first ten terms of that sequence.

Answer 1

a₁r - a₁ = -6

a₁r² - a₁r = 12

Divide the 2nd equation by the first to get r = -2

Substitute for r in the 1st equation to get a₁ = 2

The first 3 terms are 2, -4, 8

The sum of n terms of a geometric series is given by (a₁rⁿ - a₁)/(r-1).

I will leave it to you to substitute n=10 and r and a₁ into the formula to get the sum.