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If the coefficients of 5th, 6th , and 7t...

If the coefficients of 5th, 6th , and 7th terms in the expansion of `(1+x)^n` are in A.P., then `n=` a. 7 only b. 14 only c. 7 or 14 d. none of these

A

7 only

B

14 only

C

7 or 14

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( n \) such that the coefficients of the 5th, 6th, and 7th terms in the expansion of \( (1+x)^n \) are in Arithmetic Progression (A.P.). ### Step-by-Step Solution: 1. **Identify the Coefficients**: The coefficients of the 5th, 6th, and 7th terms in the expansion of \( (1+x)^n \) can be expressed using the binomial coefficient: - Coefficient of the 5th term: \( \binom{n}{4} \) - Coefficient of the 6th term: \( \binom{n}{5} \) ...
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