Question

Which term has greatest coefficient in the expansion of $(1+2 x / 3)^{15} ?$

• A. $5^{\text {th }}$
• B. $6^{\text {th }}$
• C. $7^{\text {th }}$
• D. $8^{\text {th }}$

Answer 1

Answer: (A)

The greatest coefficient is equal to the greatest term when $x= 1$.
For $x=1, \frac{T_{r+1}}{T_{r}}=\frac{15-r+1}{r} \times \frac{2}{3}$
Let $\frac{T_{r+1}}{T_{r}} \geq 1$
or $ \frac{15-r+1}{r} \frac{2}{3} \geq 1$
or $ 32-2 r \geq 3 r$
or $ r \leq 32 / 5$
or $ r=6$
Hence, $7^{\text {th }}$ term has the greatest coefficient and its value is $T_{6+1}={ }^{15} C_{6}(2 / 3)^{6}$