NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 2(i)

Question:

Find the sums given below : 7 + 10(1/2)+14+....+84

Given:

Arithmetic progression: 7, 10.5, 14, ..., 84

To Find:

The sum of the given arithmetic progression.

Formula:

Sum of an arithmetic progression = n2(a + l), where 

n is the number of terms, 

a is the first term, and 

l is the last term.

Solution:

First term (a) = 7

Common difference (d) = 10.5 - 7 = 3.5

Last term (l) = 84

To find n, we use the formula: l = a + (n-1)d 

⇒ 84 = 7 + (n-1)3.5 

⇒ 77 = (n-1)3.5 

⇒ n-1 = 773.5 = 22 

⇒ n = 22+1

⇒ n = 23

Now, we can find the sum using the formula: S_n = n2(a + l) 

⇒ S_n = 232(7 + 84) 

⇒ S_n = 232(91) 

⇒ S_n = 23 × 45.5 

⇒ S_n = 1046.5

Result:

The sum of the given arithmetic progression is 1046.5

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 2(ii)

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.