Verified answer

In a geometric series, you are multiplying each successive term by a constant. Let y be the constant. The series then becomes: 8, 8y, 8y², 8y³, 8y⁴, 8y⁵

The last term is 8y⁵ and this is equal to 134,456. Solve for y.

8y⁵ = 134,456

y⁵ = 134,456 / 8 = 16807

y= 16807 ^ (1/5) = 7

If y is 7, then the series becomes:

8, 56, 392, 2744, 19208; 134456

Adding all these numbers together yields: 156,864

a(n) = a(1) * r^(n - 1)

a(6) = 8 * r^(6 - 1)

134,456 = 8 * r^5

r^5 = 134,456 / 8

r^5 = 16,807

r = 16,807^(1/5)

r = 7

S = a(1) * (1 - r^n) / (1 - r)

S = 8 * (1 - 7^6) / (1 - 7)

S = 8 * (1 - 117649) / (-6)

S = 8 * (-117648) / (-6)

S = 8 * 19608

S = 156,864

(134,456/8)^(1/5) = 7

5

∑ 8 * 7^(k-1) = 8 (7^6 - 1) / (7-1) = 156,864

k=0