NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 2(ii)

Question:

Choose the correct choice in the following and justify : 11th term of the AP: – 3, -1/2 , 2, . . ., is (A) 28 (B) 22 (C) -38 (D) –48 1/2

Given:

Arithmetic Progression (AP): – 3, -12 , 2, . . .

To Find:

The 11th term of the given AP.

Formula:

The nth term of an AP is given by a_n = a + (n-1)d, where a is the first term and d is the common difference.

Solution:

First term, a = -3

Common difference, d = \( \frac{-1}{2} - (-3)\)

⇒ d = \( \frac{-1}{2} + 3 \)

⇒ d = \( 3 - \frac{1}{2} \)

⇒ d = \( \frac{6-1}{2} \)

⇒ d = \( \frac{5}{2} \)

We need to find the 11th term, so n = 11.

Using the formula a_n = a + (n-1)d 

⇒ a₁₁ = -3 + (11-1) × 52 = -3 + 10 × 52 = -3 + 25 = 22

Result:

The 11th term of the AP is 22. Therefore, the correct option is (B).

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 3(i)

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