Let the sum of an infinite G . P . , whose first term is a and the common ratio is r , be 5 . Let the sum of its first five terms be 98 25 . Then the sum of the first 21 terms of an AP , whose first term is 10 a r , n th term is a n and the

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Let the sum of an infinite G . P . , whose first term is a and the common ratio is r , be 5 . Let the sum of its first five terms be 98 25 . Then the sum of the first 21 terms of an AP , whose first term is 10 a r , n th term is a n and the common difference is 10 ar 2 , is equal to

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Correct answer: A. 21 a 11

For the infinite G.P. S &#8734; = a 1 - r = 5 Also a + a r + a r 2 + a r 3 + a r 4 = 5 &#8658; a 1 - r 5 1 - r = 98 25 i.e. 1 - r 5 = 98 125 &#8658; r 5 = 3 3 5 3 &#8658; r = 3 5 3 5 Now S 21 = 21 2 20 a r + 21 - 1 10 a r 2 = 21 10 a r + 100 a r 2 = 21 &#183; a 11

Let the sum of an infinite G . P . , whose first term is a and the common ratio is r , be 5 . Let the sum of its first five terms be 98 25 . Then the sum of the first 21 terms of an AP , whose first term is 10 a r , n th term is a n and the common difference is 10 ar 2 , is equal to

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