AP EAMCET · Maths · Sequences and Series
Let \(n\) be a positive integer. If the coefficients of \(2^{\text {nd }}, 3^{\text {rd }}\) and \(4^{\text {th }}\) terms in the expansion of \((1+x)^n\) are in A.P, then the value of \(n=\)
- A 6
- B 7
- C 8
- D 9
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
\(C_2 = \binom{n}{1}\), \(C_3 = \binom{n}{2}\), \(C_4 = \binom{n}{3}\) \(2C_3 = C_2 + C_4\) \(2\binom{n}{2} = \binom{n}{1} + \binom{n}{3}\) \(2 \frac{n(n-1)}{2} = n + \frac{n(n-1)(n-2)}{6}\) \(n(n-1) = n + \frac{n(n-1)(n-2)}{6}\) \(n-1 = 1 + \frac{(n-1)(n-2)}{6}\) (since…
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