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

Question:

Choose the correct choice in the following and justify : 30th term of the AP: 10, 7, 4, . . . , is (A) 97 (B) 77 (C) –77 (D) – 87

Given:

An Arithmetic Progression (AP): 10, 7, 4, ...

To Find:

The 30th 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:

Here, the first term a = 10 and the common difference d = 7 - 10 = -3.

We need to find the 30th term, so n = 30.

Using the formula a_n = a + (n-1)d, we have:

a₃₀ = 10 + (30 - 1)(-3)

⇒ a₃₀ = 10 + (29)(-3)

⇒ a₃₀ = 10 - 87

⇒ a₃₀ = -77

Result:

Therefore, the 30th term of the AP is -77. The correct option is (C).

Next question solution:

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

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