In a geometric progression, if the ratio of the sum of first $ 5 $ terms to the sum of their reciprocals is $ 49 $, and the sum of the first and the third term is $ 35 $. Then the first term of this geometric progression is

Question

In a geometric progression, if the ratio of the sum of first $ 5 $ terms to the sum of their reciprocals is $ 49 $, and the sum of the first and the third term is $ 35 $. Then the first term of this geometric progression is, $ 28 $, $ 21 $, $ 7 $, $ 42 $

MARKS App · Accepted Answer

a + a r + a r 2 + a r 3 + a r 4 1 a + 1 a r + 1 a r 2 + 1 a r 3 + 1 a r 4 = 49 ⇒ a 1 + r + r 2 + r 3 + r 4 1 a r 4 r 4 + r 3 + r 2 + r + 1 = 49 ⇒ a 2 r 4 = 4 9 ⇒ a r 2 = 7 ⇒ T 3 = 7 T 1 + T 3 = 3 5 T 1 + 7 = 3 5 T 1 = 2 8

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