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Question
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Solution
Let a and r be the first term and the common ratio of the G.P. respectively.
∴ a = 1
a3 = ar2 = r2
a5 = ar4 = r4
∴ r2 + r4 = 90
⇒ r4 + r2 – 90 = 0
= `r^2 = (-1 + sqrt(1 + 360))/2 = (-1± sqrt361)/2 =(-1 ± 19)/(2) = -10 or 9`
∴ r = ± 3 (Taking real roots)
Thus, the common ratio of the G.P. is ±3.
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