the sum of the first two term of a gp is x and the sum of the last two term of the gp is y,find the common ratio

Answer 1

If there are n terms, we have

a + ar = x
ar^(n-2) + ar^(n-1) = y

a(1+r) = x
ar^(n-2)(1+r) = y

now divide

r^(n-2) = y/x
r = (y/x)^(n-2)