Home
Class 12
MATHS
The coefficients of three consecutive te...

The coefficients of three consecutive terms of `(1+x)^(n+5)` are in the ratio 5:10:14. Then `n=` ___________.

Text Solution

Verified by Experts

Let `T_(r-1), T_(r), T_(r+1)` are three consecutive term of `(1+x)^(n+5)`
`T_(r-1) = .^(n+5)C_(r-2) (x)^(r-2), T_(r) = .^(n+5)C_(r-1)x^(r-1),T_(r+1)=.^(n+5)C_(r)x^(r)`,
where `.^(n+5)C_(r-20)`: `.^(n+5)C_(r-1)` : `.^(n+5)C_(r) = 5 : 10 : 14`.
So, `(.^(n+5)C_(r-2))/(5)= (.^(n+5)C_(r-1))/(10) = (.^(n+5)C_(r))/(14)`
Comparing first two results we have `n - 3r = -9 " "(1)`
Corrparing last two results we have `5n - 12r = -30 " "(2)`
From equation (1) and (2), `n = 6`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Single correct Answer|62 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Numerical)|24 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

The coefficients of three consecutive terms in the expansion of (1+x)^(n) are in the ratio 1:7:42. Find n.

The coefficients of three consecutive terms in the expansion of (1+a)^(n) are in the ratio 1:7:42. Find n.

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion (1+x)^(n+5) are in the ratio 5:10:14 , then the largest coefficient in this expansion is :

If the coefficients of three consecutive terms in the expansion of (1+x)^(n) are in the ratio 1:7:42, then find the value of n.

If the coefficients of three consecutive terms in the expansion of (1 + x)^(n) are in the ratio 1 : 3 : 5, then show that n = 7.

The coefficient of three consecutive terms in the expansion of (1 + x)^(n ) are in the ratio 1 : 6 : 30. Find n.

The coefficients of three consecutive terms in the expansion of (1+x)^(n) are in the ratio 182:84:30. prove that n=18