This question was uploaded on 11/11/21 on social media accounts.
This question is from IIT JEE Mains exam.
Solution:
Given, S = 4;
\[r=\frac{a_2}{a_1}=\frac3{4a_1}\]
This is an infinite sum with finite sum:
\[\Rightarrow S = \frac{a_1}{1-r}\]
\[\Rightarrow 4 = \frac{a_1}{1-\frac3{4a_1}}\]
\[\Rightarrow a_1=1⠀or⠀3\]
\[\Rightarrow r=\frac34⠀or⠀\frac14\]
\[\Rightarrow (a_1,r)=\left(1,\frac34\right)⠀or⠀\left(3,\frac14\right)\]
