If nC4 , nC5 and nC6 are in A.P., then n isa)7 or 14b)7c)14d)14 or 21Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Isme answer nikalna lengthy he isliye exam me option put karke karna padega isliye fast Hoga

Answer

Answer

Explanation:

To solve this problem, let's first understand the concept of arithmetic progression (AP).

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In other words, if we have a sequence a, a + d, a + 2d, a + 3d, ..., where a is the first term and d is the common difference, then the sequence is said to be an arithmetic progression.

Now, let's apply this concept to the given problem.

We are given that nC4, nC5, and nC6 are in arithmetic progression. This means that the differences between consecutive terms are constant.

Let's consider nC4, nC5, and nC6 as the terms of an arithmetic progression. We can write the differences between consecutive terms as follows:

Difference between nC5 and nC4 = (nC5) - (nC4)
Difference between nC6 and nC5 = (nC6) - (nC5)

Since the differences between consecutive terms are constant, we can equate these two expressions:

(nC5) - (nC4) = (nC6) - (nC5)

Simplifying this equation, we get:

(nC5) + (nC5) = (nC6) + (nC4)
2(nC5) = (nC6) + (nC4)

Now, let's expand the binomial coefficients using their formula:

2 * (n! / (5!(n-5)!)) = (n! / (6!(n-6)!)) + (n! / (4!(n-4)!))

Simplifying further, we get:

2 * (n! / (5!(n-5)!)) = (n! / (6 * 5!(n-6)!)) + (n! / (4 * 3!(n-4)!))

Cancelling out the common terms, we have:

2 / 5!(n-5)! = 1 / (6 * 5!(n-6)!) + 1 / (4 * 3!(n-4)!)

Now, let's simplify the equation further by multiplying through by common denominators:

2 / (5!(n-5)!) = (4 * 3!(n-4)! + 6 * 5!(n-6)! ) / (4 * 3!(n-4)! * 6 * 5!(n-6)!)

Cancelling out the common terms, we get:

2 = 4 * (n-4) + 6 * (n-6)

Simplifying this equation, we have:

2 = 4n - 16 + 6n - 36
2 = 10n - 52
10n = 54
n = 54/10
n = 5.4

Since n represents a number of objects, it must be a whole number. Therefore, n can only be 7 or 14.

Hence, the correct answer is option 'A' - n is 7 or 14.

Answer

2b=a+c

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