Sequence and Series
Infinite Geometric Series
JEE Main 2021
Grade 11
Question:
If the sum of an infinite G.P. is 15 and the sum of squares of its terms is 150, then the sum of $ar^2 + ar^4 + ar^6 + \dots$ is:
(1) $1$
(2) $\frac{1}{2}$
(3) $\frac{3}{2}$
(4) $\frac{5}{2}$
Step-by-Step Solution
Key Concept: $S = a/(1 - r) = 15$ and sum of squares $= a^2/(1 - r^2) = 150$. Divide: $a/(1 + r) = 10$. Solve for $r$, then find $ar^2/(1 - r^2)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)