SATHEE: Binomial Theorem 1 Question 26

Binomial Theorem 1 Question 26

28.

Let $n$ be a positive integer. If the coefficients of $2 nd, 3 rd$ , and 4th terms in the expansion of $(1 + x)^{n}$ are in AP, then the value of $n$ is… .

(1994, 2M)

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Answer:

Correct Answer: 28. $(n = 7)$

Solution:

Let the coefficients of $2$ nd, $3$ rd and $4$ th terms in the expansion of $(1 + x)^{n}$ is $^{n} C_{1},^{n} C_{2},^{n} C_{3}$ .

According to given condition,

$2 (^{n} C_{2}) =^{n} C_{1} +^{n} C_{3}$

$\Rightarrow 2 \frac{n (n - 1)}{1 \cdot 2} = n + \frac{n (n - 1) (n - 2)}{1 \cdot 2 \cdot 3}$

$\Rightarrow n - 1 = 1 + \frac{(n - 1) (n - 2)}{6}$

$\Rightarrow n - 1 = 1 + \frac{n^{2} - 3 n + 2}{6}$

$\Rightarrow 6 n - 6 = 6 + n^{2} - 3 n + 2$

$\Rightarrow n^{2} - 9 n + 14 = 0$

$\Rightarrow (n - 2) (n - 7) = 0$

$\Rightarrow n = 2$

$or n = 7$

But $^{n} C_{3}$ is true for $n \geq 3$ , therefore $n = 7$ is the answer.

Binomial Theorem 1 Question 26

28.

Answer:

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Binomial Theorem 1 Question 26

28.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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