In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 703 and the product of the third and fifth terms is 49 . Then the sum of the 4^ th ,6^ th and 8^ th…

Question

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 703 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 :

Accepted Answer

Correct answer: B. (b) T_2+T_6= 703 ar+ ar^5= 703 T_3 T_5=49 ar^2 ar^4=49a^2r^6=49 ar^3=+7 ,a= 7r^3 ar ⁡(1+r^4)= 703 7r^2(1+r^4)= 703 ,r^2=t 1t(1+t^2)= 1033t^2-10t+3=0t=3 , 13 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

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

Solution

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