In a gp the product of the 2nd and the 4th term is doubled the 5th term & the sum of the first four term is 80.find the gp

Answer 1

I will read that as:
the product of the 2nd and the 4th term is double the 5th term
---> (ar)(ar^3) = 2(ar^4)
a^2 r^4 = 2ar^4
divide by ar^4
a = 2

the sum of the first four term is 80
---> a(r^4 - 1)/(r - 1) = 80
but a = 2, so
r^4 - 1 = 40(r - 1)
r^4 - 40r + 39 = 0
r = 3, r = 1, or r = two complex roots
but in a GP, r ≠ 1
so r = 3

Answer 2

pressed <submit> too soon, but I am sure you can state the GP.