Question bank/JEE Main/Mathematics

Let (1 + x)^n = 1 + a_1x + a_2x^2 +...+ a_nx^n. If a_1,
a_2 and a_3 are in AP, then the value of n is

A4B5C6D7

Show answer and solution▾

[IMAGE] $\because$ a_1, a_2 and a_3 are in AP.
$\therefore$ 2a_2 = a_1 + a_3 [IMAGE] $\Rightarrow 2 \cdot \frac{n(n - 1)}{2!} = n + \frac{n(n - 1)(n - 2)}{3!}$
$\Rightarrow$ n^2 - 9n + 14 = 0
$\Rightarrow$ (n - 2) (n -7) = 0
$\therefore$ n = 7

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx