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CGP EDU Academic Team
Published on: August 14, 2026
The sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45. Find the series.
Text Solution
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Sol. Let 'a' be the first term and 'r' be the common ratio. Sum = 15 ⇒ (a + ar + ar 2 + .... ∞ ) = 15
⇒ 
= 15 ...(i)
Sum of the squares = 45
⇒ (a 2 + a 2 r 2 + a 2 r 4 + .... ∞ ) = 45
⇒ 
= 45 ....(ii)
Dividing the square of (i), by (ii),
= 
⇒ 
= 5 ⇒ 6r = 4 ⇒ r = 2/3
Putting r = 2/3 in (i),
= 15 ⇒ a = 5
The required series is
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