In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 3 70 and the product of the third and fifth terms is 49 . Then the sum of the 4 th , 6 th and 8 th

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In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 3 70 ​ and the product of the third and fifth terms is 49 . Then the sum of the 4 th , 6 th and 8 th terms is equal to :

TestHub · Accepted Answer

T 2 ​ + T 6 ​ = 3 70 ​ ar + ar 5 = 3 70 ​ T 3 ​ ⋅ T 5 ​ = 49 ar 2 ⋅ ar 4 = 49 a 2 r 6 = 49 ar 3 = + 7 , a = r 3 7 ​ ar ( 1 + r 4 ) = 3 70 ​ r 2 7 ​ ( 1 + r 4 ) = 3 70 ​ , r 2 = t t 1 ​ ( 1 + t 2 ) = 3 10 ​ 3 t 2 − 10 t + 3 = 0 t = 3 , 3 1 ​ Increasing G.P. r 2 = 3 , r = 3 ​ T 4 ​ + T 6 ​ + T 8 ​ = ar 3 + ar 5 + ar 7 = ar 3 ( 1 + r 2 + r 4 ) = 7 ( 1 + 3 + 9 ) = 91

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