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:

Step-by-step solution

According to Question S₅ S₅^ =49 (here, S₅= Sum of first 5 terms and S₅= Sum of their reciprocals) aligned & a (r^5-1 ) (r-1) a⁻¹ (r⁻⁵-1 ) (r⁻¹-1 ) =49 & a (r^5-1 ) (r⁻¹-1 ) a⁻¹ (r⁻⁵-1 ) (r-1) =49 & or a^2 (1-r^5 ) (1-r) r^5 (1-r^5 ) (1- r ) r =49 & a^2 r^4=49 a^2 r^4=7^2 & a r^2=7 aligned Also, given, S₁+S₃=35a+a r^2=35 Now substituting the value of eq. (1) in eq. (2) a+7=35a=28