Question

if the first and 8th term of a g.p.is x^-4 and x^52 and the second term is x^t then t:

Answer 1

seven steps and 56 powers of x
... so 8 powers per step

t = -4 + 8

Answer 2

given:
a= x^-4
ar^7 = x^52

use substitution:
(x^-4)r^7 = x^52
r^7 = x^59
r = x^(59/7)

2nd term = ar
= (x^-4)(x^59/7)
= x^(31/7)

matching it with x^t ---> t = 31/7