Question

If in the expansion of $(a+b{)}^n$ and $(a+b{)}^{n+3}$, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C

5

n =5

Coefficients of the 2nd and 3rd terms in $(a+b{)}^n$ are ${}^n{C}_1$ and ${}^n{C}_2$

Coefficients of the 3rd and 4th terms in $(a+b{)}^{n+3}$ are ${}^{n+3}{C}_2$ and ${}^{n+3}{C}_3$

Thus, we have

$\frac{{}^n{C}_1}{{}^n{C}_2}=\frac{{}^{n+3}{C}_2}{{}^{n+3}{C}_3}$

$\Rightarrow \frac{2}{n-1}=\frac{3}{n+1}$

$\Rightarrow 2n+2=3n-3$

$\Rightarrow n=5$