Question:
If the coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P. then n =
If the coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P. then n =
Updated On: Apr 27, 2024
- 7
- 14
- 7 or 14
- 8
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The Correct Option is C
Solution and Explanation
$n^2 - (4r + 1) n + 4r^2 - 2 = 0 $ where r = 5
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Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.