Find the 8th term of each geometric sequence with the given terms

Question

A15 = 100 and A17 = 25

Answer 1

First you have to find the common ratio A17=A15(x^2)

25=100(x^2)

x^2=1/4

x=1/2 or .5

To have gone from the 8th term to the 15th term we would have had to multiply the 8th term 7 times by our common ratio of 1/2

So A8(.5^7) = A15

A8 = 100/.5^7

A8=12,800

An Alternate way to do this would b to use general formula An= A1(r^n-1) where An is a15 or 100. This will allow you to solve for A1 and can use this to solve for A8