InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
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. 2B. 7C. 11D. 14 |
|
Answer» 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` |
|