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.

Asked by Abhisek | 2 years ago |  93

##### Solution :-

Let’s consider a and r to be the first term and the common ratio of the G.P. respectively.

Given, a = 1

a3 = ar2 = r2

a5 = ar4 = r4

Then, from the question we have

r2 + r4 = 90

r4 + r2 – 90 = 0

$$r^2=\dfrac{-1+\sqrt{1+360}}{2}$$

$$\dfrac{-1\pm\sqrt{1+360}}{2}$$

$$\dfrac{-1\pm19}{2}$$

= -10 or 9

$$r\pm3$$

Answered by Pragya Singh | 2 years ago

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