If the coefficient of the second, third and f | vedclass

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Question

(a) In the expansion of ${(1 + x)^n}$, it is given that $^n{C_1}{,^n}{C_2}{,^n}{C_3}$ are in $A.P.$

==> ${2.^n}{C_2} = {\,^n}{C_1} + {\,^n}{C_3}

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(a) In the expansion of ${(1 + x)^n}$, it is given that $^n{C_1}{,^n}{C_2}{,^n}{C_3}$ are in $A.P.$

==> ${2.^n}{C_2} = {\,^n}{C_1} + {\,^n}{C_3}$

==> $2.\frac{{n(n - 1)}}{{1.2}} = \frac{n}{1} + \frac{{n(n - 1)(n - 2)}}{{1.2.3}}$

==> $6(n - 1) = 6 + (n - 2)(n - 1)$

==> ${n^2} - 9n + 14 = 0$

==> $n = 2$or $n = 7$.

But $n = 2$ is not acceptable because, when $n=2$, there are only three terms in the expansion of ${(1 + x)^2}$, $	herefore $ $n = 7$.

If the coefficient of the second, third and fourth terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then $n$ is equal to

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