NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 9

Question:

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Given:

Sum of first 7 terms (S₇) = 49
Sum of first 17 terms (S₁₇) = 289

To Find:

Sum of first n terms (S_n)

Formula:

Sum of n terms of an AP: S_n = n2[2a + (n-1)d]

Solution:

S₇ = 72[2a + 6d] = 49 ⇒ 2a + 6d = 14 (1)

S₁₇ = 172[2a + 16d] = 289 ⇒ 2a + 16d = 34 (2)

Subtracting (1) from (2): 10d = 20 

⇒ d = 2

Substituting d = 2 in (1): 

2a + 6(2) = 14 

⇒ 2a = 2 

⇒ a = 1

Substitute a = 1 in S_n 

⇒ S_n = n2 [2(1) + (n-1)2] 

⇒ S_n = n2 [2 + 2n -2] 

⇒ S_n = n2 [2n] = n²

⇒ S_n =
n x n 

⇒ S_n = n²

Result:

The sum of first n terms is n²

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 10(i)

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