The sum of the first three terms of a G.P is 16 and the sum of the next three terms is 128. Determine the first term, common ratio and the sum to n terms of the G.P.
The sum of the first three terms of a G.P is 16 and the sum of the next three terms is 128. Determine the first term, common ratio and the sum to n terms of the G.P.
Let the three terms be a, ar, ar2.
a + ar + ar2 = 16 ………………………(i)
Let the next three terms be ar3, ar4, ar5.
ar3 + ar4 + ar5 = 128
r3(a + ar + ar2) = 128
r3(16) = 128 (from i)
r3 = 8
r = 2
Therefore the common ratio is 2.
Substituting r = 2 in (i)
a + 2a + 4a = 16
7a = 16
a = 16/7
Sn =
Therefore the first term is 16/7, common ratio is 2 and sum to n terms is
.
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and their product is 1. Find the common ratio and the terms.