wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Let n be a positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of (1+x)n are in AP, then the value of n is___

Open in App
Solution

The coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)n is nC1, nC2, nC3
According to the given condition,
2(nC2)=nC1+nC3 2n(n1)1.2=n+n(n1)(n2)1.2.3 n1=1+(n1)(n2)6 n1=1+n23n+26 6n6=6+n23n+2 n29n+14=0 (n2)(n7)=0 n=2,7

But nC3 is true for n 3, therefore n = 7 is the answer.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
How to Expand?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon