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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
Options
3
4
5
6
Solution
n = 5
\[\text{ Coefficients of the 2nd and 3rd terms in } (a + b )^n \text{ are } ^{n}{}{C}_1 \text{ and } ^{n}{}{C}_2 \]
\[\text{ Coefficients of the 3rd and 4th terms in } (a + b )^{n + 3} \text{ are } ^{n + 3}{}{C}_2 \text{ and }^{n + 3}{}{C}_3 \]
\[\text{ Thus, we have} \]
\[\frac{^{n}{}{C}_1}{^{n}{}{C}_2} = \frac{^{n + 3}{}{C}_2}{^{n + 3}{}{C}_3}\]
\[ \Rightarrow \frac{2}{n - 1} = \frac{3}{n + 1}\]
\[ \Rightarrow 2n + 2 = 3n - 3\]
\[ \Rightarrow n = 5\]
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