NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 12

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 12

Question:

Find the sum of the first 40 positive integers divisible by 6.

Given:

We need to find the sum of the first 40 positive integers divisible by 6.

To Find:

The sum of the first 40 positive integers divisible by 6.

Formula:

The sum of an arithmetic series is given by: Sn = n 2 (a1 + an), where 

n is the number of terms, 

a1 is the first term, and 

an is the last term.

Solution:

The first 40 positive integers divisible by 6 are 6, 12, 18, ..., 240.

This is an arithmetic series with 

first term a1 = 6, 

common difference d = 6, and 

number of terms n = 40.

The last term is a40

⇒ a40 = a1 + (n-1)d 

⇒ a40 = 6 + (40-1)6 

⇒ a40 = 6 + 39(6) 

⇒ a40 = 240.

Using the formula for the sum of an arithmetic series: Sn = n 2 (a1 + an),

⇒ S40 = 40 2 (6 + 240) 

⇒ S40 = 20(246) 

⇒ S40 = 4920.

Result:

The sum of the first 40 positive integers divisible by 6 is 4920.

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