Home
Class 11
MATHS
If the coefficients of 2nd, 3rd and 4th ...

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 n.

A

2

B

7

C

11

D

14

Text Solution

Verified by Experts

The correct Answer is:
B
The expansion of `(1 + x)^(n) " is " .^(n)C_(0) + .^(n)C_(1) x + .^(n)C_(2) x^(2) + .^(n)C_(3) x^(3) + .... + .^(n)C_(n) x^(n)`
`:.` Coefficient of 2nd term `= .^(n)C_(1)`,
Coefficient of 3 rd term `= .^(n)C_(2)`,
and coefficient of 4 th term `= .^(n)C_(3)`
Given that, `.^(n)C_(1), .^(n)C_(2) " and " .^(n)C_(3)` are in AP.
`:. 2 .^(n)C_(2) = .^(n)C_(1) + .^(n)C_(3)`
`rArr 2[((n)!)/((n - 2)! 2!)] = ((n)!)/((n - 1)!) + ((n)!)/(3! (n - 3)!)`
`rArr (2.n (n - 1) (n - 2)!)/((n - 2)! 2!) = (n (n - 1)!)/((n - 1)!) + (n (n - 1) (n - 2) (n - 3)!)/(3.2.1 (n - 3)!)`
`rArr n (n - 1) = n + (n (n - 1) (n - 2))/(6)`
`rArr 6n - 6 = 6 + n^(2) - 3n + 2`
`rArr n^(2) - 9n + 14 = 0`
`rArr n^(2) - 7n - 2n + 14 = 0`
`rArr n(n - 7) - 2 (n - 7) = 0`
`:. n = 2 " or " n = 7`
Sine, `n = 2` is not possible
`:. n = 7`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise Long Answer type question|6 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

Similar Questions

Explore conceptually related problems

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

If the coefficients of 2nd,3rd and 4th terms in the expansion of (1+x)^(n),nN are in A.P. then n=7b.14c.2d .none of these

The coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n are in A.P. Find the value of n.

17.If the coefficients of 2nd,3rd and 4th terms in the expansion of (1+x)^(2n) are in A.P. Show that 2n^(2)-9n+7=0

If the coefficients of 5^(th), 6^(th) and 7^(th) terms in the expansion of (1+x)^(n) are in A.P. then n =