Find common ratio - Geometric series

Question

The sum of the first seven terms in a geometric series is 7. The sum of the next seven terms is 896. Find the common ratio.

Answer 1

7 = a₁(1 - r⁷) / (1 - r)

896 = a₈(1 - r⁷) / (1 - r)

7 / a₁ = 896 / a₈

7a₈ = 896a₁

7(a₁r⁷) = 896a₁

7r⁷ = 896

r⁷ = 128

r = 2