Q: If the sum of the coefficients in the expansion of (1 + 2x)^{n} is 6561, the greatest term in the expansion for x = 1/2 is

(A) 4th

(B) 5th

(C) 6th

(D) none of these

**Click to See Answer : **

Sol. sum of the coefficient in the expansion of (1 + 2x)

^{n}= 6561⇒ (1 + 2x)^{n} = 6561, when x = 1

⇒ 3^{n} = 6561

⇒ 3^{n} = 3^{8}

⇒ n = 8

$\large \frac{T_{r+1}}{T_r} = \frac{8_{C_r} (2x)^r }{8_{C_{r-1}} (2x)^{r-1}} = \frac{9-r}{r} \times 2x $

Since x = 1/2 ;

$\large \frac{T_{r+1}}{T_r} = \frac{9-r}{r} $

$\large \frac{T_{r+1}}{T_r} > 1 \Rightarrow \frac{9-r}{r} >1 $

9-r > r ⇒ 2r < 9 ⇒ r < 4.5

Hence, 5^{th} term is the greatest term.

Hence (B) is the correct answer.