If the first three terms in the expansion of $(1 + a x)^{n}$ are $1, 8 x,$ $24 x^{2}$ respectively, then $a =$

1

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Solution

The correct option is A $2$
$T_{2} =^{n} C_{1} a x = 8 x$ ...(i)
$T_{3} =^{n} C_{2} a x^{2} = 24 x^{2}$ ...(i)
From (i), we get
$a n = 8$ ...(iii)
From (ii), we get
$\frac{a^{2} n (n - 1)}{2} = 24$
$\frac{a n (a n - a)}{2} = 24$
$8 (8 - a) = 48$ ...from (iii)
$8 - a = 6$
$a = 2$

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