Sequence and Series
Geometric Progression
JEE Main 2021
Grade 11
Question:
In an increasing G.P. of positive terms, $a_2 + a_6 = \frac{25}{2}$ and $a_3 \cdot a_5 = 25$. Then $a_4 + a_6 + a_8$ equals:
(1) $25$
(2) $35$
(3) $30$
(4) $45$
Step-by-Step Solution
Key Concept: $a_3a_5 = (ar^3)^2 = 25 \Rightarrow ar^3 = 5$ (the 4th term). Write $a_4 + a_6 + a_8 = ar^3(1 + r^2 + r^4)$. Use $a_2 + a_6 = ar(1 + r^4) = 25/2$ with $ar^3 = 5$ to find $r$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)