Question

# If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)n are in A.P., then find the value of

Solution

## Coefficients of the 2nd, 3rd and 4th term in the given expansion are: nC1,nC2 and nC3 We have: 2×nC2=nC1+nC3 Dividing both sides by nC2, we get: 2=nC1nC2+nC3nC2 ⇒2=2n−1+n−23 ⇒6n−6=6+n2+2−3n ⇒n2−9n+14=0 ⇒n=7[∵n≠2 as 2 > 3 in the 4th term] MathematicsRD SharmaStandard XI

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