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 PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Numerical|25 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

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

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 ndot

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

The three successive of the consecutive three terms in the expansion of (1+x)^(n) are in the ratio 1 : 2 : 3 . Find n .

The coefficient of the middle term in the expansion of (1+x)^(2n) is

The coefficient of x^n in the expansion of (1+x)(1-x)^n is

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

Coefficient of x^n in the expansion of (1+x)^(2n) is

The coefficient of three consecutive terms in the expansion of (1+x)^n are a, b, c respectively prove that (2ac+b(a+c))/(b^2-ac)=n .

The coefficient of the middle term of the expansion of (1-2x+x^2)^n is