Question

Find numerically the greatest term in the expansion of ${(3-5x)}^{15}$ when $x=\frac{1}{5}$

• A. $445\times 3^{12}$
• B. $445\times 3^{10}$
• C. $455\times 3^{10}$
• D. $455\times 3^{12}$

Answer 1

The correct option is D $455\times 3^{12}$

$(3-5x{)}^{15}$
$=3^{15}(1-\frac{5x}{3}{)}^{15}$
Now At $x=\frac{1}{5}$ we get
$3^{15}(1-\frac{1}{3}{)}^{15}$
Hence numerically greatest term will be given by
$r=\frac{(1+n)|x|}{1+|x|}$
$\frac{16.\frac{1}{3}}{\frac{4}{3}}$
$=4$
Hence, $T_5=3^{15}.{}^{15}{C}_4(\frac{1}{3}{)}^4$
$=3^{11}.1365$
$=455\times 3^{12}$.