The sum of first n natural numbers is given by 1/2 n² + 1/2 n. Find the sum of natural numbers from 11 to 30

Solution:

Given, the sum of first n natural numbers is given by 1/2 n² + 1/2 n

We have to find the sum of natural numbers from 11 to 30.

Sum of natural numbers from 11 to 30 = sum of first 30 natural numbers - sum of first 10 natural numbers.

Sum of first 30 natural numbers,

Put n = 30 in the given expression

1/2 n² + 1/2 n = 1/2 (30)² + 1/2 (30)

= 1/2 (900) + 1/2 (30)

= 1/2 (900 + 30)

= 1/2 (930)

= 465

Sum of first 10 natural numbers,

Put n = 10 in the given expression

1/2 n² + 1/2 n = 1/2 (10)² + 1/2 (10)

= 1/2 (100) + 1/2 (10)

= 1/2 (100 + 10)

= 1/2 (110)

= 55

Sum of natural numbers from 11 to 30 = 465 - 55

= 410

Therefore, the sum of the natural numbers from 11 to 30 is 410.

✦ Try This: The sum of first n natural numbers is given by 1/2 n² + 1/2 n³. Find the sum of the first 10 natural numbers

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12

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NCERT Exemplar Class 7 Maths Chapter 10 Problem 86 (iii)

The sum of first n natural numbers is given by 1/2 n² + 1/2 n. Find the sum of natural numbers from 11 to 30

Summary:

The sum of first n natural numbers is given by 1/2 n² + 1/2 n. The sum of the natural numbers from 11 to 30 is 410

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