Question

In the following expansion find which is the greatest term:
${(3+2x)}^{15}$ when $x=\frac{5}{2}$.

Answer 1

$(3+2x{)}^{15}=3^{15}{(1+\frac{2}{3}x)}^{15}$

$T_{r+1}=\frac{15-r+1}{r}\cdot \frac{5}{3}\times T_r$

For $T_{r+1}>T_r$ when $80-5r>3r$ or $r<10$

Therefore $T_{10}$ and $T_{11}$ are equal and the greatest terms