Question

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

• A. $T_4$
• B. $T_3$
• C. $T_5$
• D. None of these

Answer 1

Answer: (B)

${(4-3x)}^7=4^7{\left(1-\frac{3x}{4}\right)}^2$ Consider, ${\left(1-\frac{3x}{4}\right)}^7$ $\frac{T_{r+1}}{T_r}=\frac{7-r+1}{r}.\frac{3}{4}.\frac{2}{3}\ge 1$ $\Rightarrow$ $r\le 2.66$ $\therefore$ $r=2$ Hence, the greatest term is $T_3$ .