Question

In a Gp the product of the second and the fourth term is double the fifth term and the sum of the first four term is 80. Find the first five terms of the Gp

Answer 1

Using your definitions of a GP ....
"the product of the second and the fourth term is double the fifth term "
---> (ar)(ar^3) = 2(ar^4)
a^2 r^4 = 2a r^4
a = 2

"the sum of the first four term is 80"
---> a + ar + ar^2 + ar^3 = 80
2(1 + r + r^2 + r^3) = 80
1 + r + r^2 + r^3 - 40 = 0
r^3 + r^2 + r - 39 = 0
Try ±3 and ± 13
sure enough , r = 3 satisfies the equation
did a long division and got
r^3 + r^2 + r - 39 = (r-3)(r^2 + 4r + 13)
The quadratic does not have any real roots, so r = 3

take it from there.

Answer 2

explain

Answer 3

how did u do the long division please?