The sum of the first four terms of a G.P.is 30 and that of the last four terms is 960. If the first and the last term of the G.P. are 2 and 512 respectively, find the the common ratio.

Answer 1

first term is 2
so a = 2
last term is 512
ar^(n-1) = 512
2r^(n-1) = 512
r^(n-1) = 256

a + ar + ar^2 + ar^3 = 30 , but a=2
2(1 + r + r^2 + r^3) = 30
(1 + r + r^2 + r^3) = 15 (equation #1)

ar^(n-1) + ar^(n-2)+ar^(n-3)+ar^(n-4) = 960 , remember a=2
r^(n-1) + r^(n-2)+r^(n-3)+r^(n-4) = 480
r^(n-4)(r^3 + r^2 + r + 1) = 480 (equation #2)

divide #2 by #1 ----> r^(n-4) = 480/15 = 32

now r^(n-1) / r^(n-4) = 256/32 = 8

r^3 = 8
r = 2

Answer 2

The sum of three number in G.P.is 14 and their product is -216. find the number.