NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 3 (iii)

Question

In an AP: given a₁₂ = 37, d = 3, find a and S₁₂.

Given

a₁₂ = 37, d = 3

To Find

a (first term) and S₁₂ (sum of first 12 terms)

Formula

The nth term of arithmetic progression is given by a_n = a + (n - 1)d
Sum of an arithmetic progression = S_n = n2(2a + (n - 1)d)

Solution

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

a₁₂ = a + (12 - 1)3 

⇒ 37 = a + 33 

⇒ a = 37 - 33 

⇒ a = 4

Now, using the formula S_n = n2(2a + (n - 1)d), we have:

S₁₂ = 122(2(4) + (12 - 1)3) 

⇒ S₁₂ = 6(8 + 33) 

⇒ S₁₂ = 6(41) 

⇒ S₁₂ = 246

Result

a = 4, S₁₂ = 246

Next question solution

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 3 (iv)

Explore more in Arithmetic Progressions chapter:

Click this link to explore more NCERT Class X Chapter 5 Arithmetic Progressions solutions

Explore more:

Click this link to explore more NCERT Class X chapter solutions

© Kaliyuga Ekalavya. All rights reserved.