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

Step-by-step solution

T ₂+ T ₆= 70 3 ar + ar ^5= 70 3 ~T ₃ T ₅=49 ar ^2 ar ^4=49 a ^2 r ^6=49 ar ^3=+7, a = 7 r ^3 ar (1+ r ^4 )= 70 3 7 r ^2 (1+ r ^4 )= 70 3 , r ^2= t 1 t (1+ t ^2 )= 10 3 3 t ^2-10 t +3=0 t =3, 1 3 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