Sequence and Series
Arithmetic Progression
JEE Main 2021
Grade 11
Question:
Let $S_n$ be the sum of first $n$ terms of an A.P. If $S_{3n} = 3S_{2n}$, then $\frac{S_{4n}}{S_{2n}}$ equals:
(1) $2$
(2) $4$
(3) $6$
(4) $-6$
Step-by-Step Solution
Key Concept: From $S_{3n} = 3S_{2n}$, derive a relation between $a$ and $d$ (involving $n$). Substitute the same relation into $S_{4n}$ and $S_{2n}$ and simplify the ratio.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)