NCERT Class X Chapter 5: Arithmetic Progression Example 14(i)

Question:

Find the sum of : the first 1000 positive integers

Given:

The first 1000 positive integers: 1, 2, 3, ..., 1000

To Find:

The sum of the first 1000 positive integers

Formula:

The sum of the first n positive integers is given by the formula: n(n+1) 2

Solution:

Let S be the sum of the first 1000 positive integers.

Using the formula for the sum of an arithmetic series:

S = n(n+1) 2 where n = 1000

Substituting n = 1000 into the formula:

S = 1000(1000+1) 2

S = 1000(1001) 2 ⇒ S = 1001000 2 ⇒ S = 500500

Result:

The sum of the first 1000 positive integers is 500500.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 14 (ii)

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