math
posted by Anonymous on .
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.

first term is 2
so a = 2
last term is 512
ar^(n1) = 512
2r^(n1) = 512
r^(n1) = 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^(n1) + ar^(n2)+ar^(n3)+ar^(n4) = 960 , remember a=2
r^(n1) + r^(n2)+r^(n3)+r^(n4) = 480
r^(n4)(r^3 + r^2 + r + 1) = 480 (equation #2)
divide #2 by #1 > r^(n4) = 480/15 = 32
now r^(n1) / r^(n4) = 256/32 = 8
r^3 = 8
r = 2