Home
Class 12
MATHS
The first three terms in the expansion o...

The first three terms in the expansion of `(1+a x)^n(n!=0)` are `1,6xa n d16 x^2dot` Then find the value of `aa n dndot`

Text Solution

Verified by Experts

The correct Answer is:
`a=2//3, n = 9`
`T_(1) = .^(n)C_(0)=1`
`T_(2) = .^(n)C_(1) ax = 6x " "(1)`
`T_(3) = .^(n)C_(2) (ax)^(2) = 16x^(2) " "(2)`
From (2),
`na = 6 " " (3)`
From (3),
`(n(n-1))/(2)a^(3) = 16 " "(4)`
Eliminating a from (3) and (4),
`(n-1)/(2n) = 4/9` or `n = 9`
From (3),
`a = 2//3`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.2|10 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.3|7 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

If the middle term in the expansion of (x^2+1//x)^n is 924 x^6, then find the value of ndot

The sum of the coefficients of the first three terms in the expansion of (x - 3/x^(2))^(n)x != 0 ,m being a natural number, is 559. Find the term of the expansion containing x^(3) .

If the three consecutive coefficients in the expansion of (1+x)^n are 28, 56, and 70, then the value of n is.

In the expansion of (1+x)^n , 7th and 8th terms are equal. Find the value of (7//x+6)^2 .

If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N is 15, then the value of n is equal to.

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

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

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

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

The number of real negative terms in the binomial expansion of (1+i x)^(4n-2),n in N ,x >0 is

Home
Profile