Question

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is(a) 5(b) 3/5(c) 8/5(d) 1/5

Answer 1

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Answer 2

The common ratio of the G.P. is r = $\frac{3}{5}$

Step-by-step explanation:

Let the infinite G.P. series is a + ar + ar² + ar³ + ............. up to ∞.

Now, the sum is given by $S = \frac{a}{1 - r} = 20$ ........... (1)

Again, the sum of the square of the terms of the G.P. is given by 100.

Now, the infinite G.P. becomes

$a^{2} + a^{2}r^{2} + a^{2}r^{4} + .......$ up to ∞

Now, the sum, $S' = \frac{a^{2} }{1 - r^{2} } = 100$ ........... (2)

Hence, solving equations (1) and (2) we get, $\frac{400(1 - r)^{2} }{1 - r^{2}} = 100$

⇒ 4(1 + 2r + r²) = 1 - r²

⇒ 5r² - 8r + 3 = 0

⇒ (r - 1)(5r - 3) = 0

So, r = $\frac{3}{5}$ {Since r can not be 1} (Answer)