Engineering Board Exam Reviewer · Binomial Theorem · hard

The coefficients of the 2nd, 3rd, and 4th terms in the expansion of (1+x)n are in arithmetic progression. Find n (with n≥3).

1. 7
2. 2
3. 14
4. 9

Answer

A. 7

Solution

The coefficients are n1, n2, n3. The AP condition 2 n2= n1+ n3 simplifies to n2-9n+14=0, so n=2 or n=7. For n≥3, n=7: the coefficients 7,21,35 have common difference 14.

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