Question

Find numerically the greatest term in the expansion of ${(4-3x)}^7$ when $x=\frac{2}{3}$

• A. ${14\times 4}^6$
• B. ${84\times 4}^6$
• C. ${280\times 4}^4$
• D. $4^7$

Answer 1

Answer: (A)

${14\times 4}^6$

given expansion is ${(4-3x)}^7$ when $x=\frac{2}{3}$

To find the numerically greatest term for the general expansion ${(x+y)}^n$ where $x,y>0$ and $n$ is a natural number,

We need to find $\alpha =\frac{(n+1)y}{x+y}$,

Here $\alpha =\frac{8\left(\frac{2}{3}.3\right)}{4+2}=2.67$,

As $\alpha$ is not an integer the numerically greatest term is the integral part of $\alpha$ i.e., $\left[\alpha \right]=2$,

$⟹t_2=\left(\begin{array}{c}7\\ 1\end{array}\right)4^{6}2=14.4^6$ is numerically greatest term.