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

Question

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, 21 a 11, 22 a 11, 15 a 16, 14 a 16

MARKS App · Accepted Answer

For the infinite G.P. S ∞ = a 1 - r = 5 Also a + a r + a r 2 + a r 3 + a r 4 = 5 ⇒ a 1 - r 5 1 - r = 98 25 i.e. 1 - r 5 = 98 125 ⇒ r 5 = 3 3 5 3 ⇒ 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 · a 11

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