Binomial Theorem
Properties of Binomial Coefficients
JEE Main 2018
Grade 11
Question:
If the coefficients of the $2^{\text{nd}}, 3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion of $(1 + x)^n$ are in A.P., then $n$ equals:
(1) $5$
(2) $6$
(3) $7$
(4) $9$
Step-by-Step Solution
Key Concept: Write the three coefficients as $\binom{n}{1}, \binom{n}{2}, \binom{n}{3}$, impose the A.P. condition $2\binom{n}{2} = \binom{n}{1} + \binom{n}{3}$, and solve the resulting quadratic in $n$ (rejecting the trivial root).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)