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Question: The sum of an infinite GP is 23 and the sum of squares of the series is 69, the first term is –...

The sum of an infinite GP is 23 and the sum of squares of the series is 69, the first term is –

A

69/13

B

10/3

C

9/10

D

None

Answer

69/13

Explanation

Solution

r = x2−yx2+y\frac { x ^ { 2 } - y } { x ^ { 2 } + y } = 529−69529+69\frac { 529 - 69 } { 529 + 69 } = 460598\frac { 460 } { 598 }

Q x = Ž a = (1 – r) = 23. 138598\frac { 138 } { 598 } = 23. 313\frac { 3 } { 13 }