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If \({ }^n C_4,{ }^n C_5\) and \({ }^n C_6\) are in A.P., then \(n\) is
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Verified Answer
The correct answer is:
7 or 14
Hints: \({ }^n \mathrm{C}_4,{ }^n \mathrm{C}_5,{ }^n \mathrm{C}_6\) are in \(\mathrm{AP}\)
\(\begin{aligned}
& \text { 2. }{ }^n \mathrm{C}_5={ }^n \mathrm{C}_4+{ }^n \mathrm{C}_6 \\
& \frac{2}{5(n-5)}=\frac{1}{(n-4)}+\frac{1}{30} \\
&
\end{aligned}\)
by solving \(n=14\) or 7
\(\begin{aligned}
& \text { 2. }{ }^n \mathrm{C}_5={ }^n \mathrm{C}_4+{ }^n \mathrm{C}_6 \\
& \frac{2}{5(n-5)}=\frac{1}{(n-4)}+\frac{1}{30} \\
&
\end{aligned}\)
by solving \(n=14\) or 7
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