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

Question:

In an AP: given a = 7, a₁₃ = 35, find d and S₁₃.

Given:

a = 7, a₁₃ = 35

To Find:

d and S₁₃

Formula:

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

Solution:

a₁₃ = a + (13 - 1)d 

⇒ 35 = 7 + 12d 

⇒ 12d = 28 

⇒ d = 28 12  

⇒ d = 7 3

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

⇒ S₁₃ = 13 2 (2(7) + (13 - 1) 7 3 ) 

⇒ S₁₃ = 13 2 (14 + 12 × 7 3 ) 

⇒ S₁₃ = 13 2 (14 + 28) 

⇒ S₁₃ = 13 2 (42) 

⇒ S₁₃ = 13 × 21 

⇒ S₁₃ = 273

Result:

d = 7 3 , S₁₃ = 273

Next question solution:

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

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