the fifth term and the sum of the first five terms of a geometric sequence are 81 and 61 respectively. determine the common ratio and the first term of the sequence
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Given a GP.
The second term = ar = 81/2 …(1)
The fifth term = ar^4 = 1/6 …(2)
Divide (2) by (1)
r^3 = (1/6)/(81/2) = (1*2/6*81) = (1/243) or
r = 1/6.240251469 = 0.160249952 and
a = 252.7301845.
The first term is a = 252.7301845, and the common ratio is r = 0.160249952.
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