Question

Find the numerically greatest term in the expansion of $(2+3x{)}^9$, when x=$\frac{3}{2}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let $T_{r+1}$ be the numerically greatest term. Then
$r=[\frac{(n+1)}{(1+|\frac{x}{y}|)}]$

$\Rightarrow r=[\frac{9+1}{(1+|\frac{2}{3x}|)}]$

$\Rightarrow r=[\frac{10}{(1+|\frac{2\times 2}{3\times 3}|)}]$

$\Rightarrow r=[\frac{10\times 9}{9+4}]$

$\Rightarrow r=6$
$\Rightarrow T_7$ has the greatest coefficient.

$T_7={}^9{C}_6{2}^3(3\times \frac{3}{2}{)}^6$
$={}^9{C}_6{2}^9(\frac{3}{2}{)}^{12}$