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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

${16^{th}}$ term in the expansion of ${(\sqrt x - \sqrt y )^{17}}$ is

The positive value of $a$ so that the co-efficient of $x^5$ is equal to that of $x^{15}$ in the expansion of ${\left( {{x^2}\,\, + \,\,\frac{a}{{{x^3}}}} \right)^{10}}$ is

Write the general term in the expansion of $\left(x^{2}-y\right)^{6}$

If the term independent of $x$ in the exapansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9}$ is $k,$ then $18 k$ is equal to

Let $\mathrm{m}$ and $\mathrm{n}$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac{1}{3} \mathrm{x}^{\frac{1}{3}}+\frac{1}{2 \mathrm{x}^{\frac{2}{3}}}\right)^{18}$. Then $\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^{\frac{1}{3}}$ is :