Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

Solution:

Given, the series is a multiple of 2 as well as 5.

We have to find the sum of the integers between 1 and 500 which are multiples of 2 as well as 5.

Taking the LCM of 2 and 5 = 10

So, the series is a multiple of 10.

The series is 10, 20, 30,.........,490.

The nth term of the series in AP is given by

aₙ = a + (n - 1)d

Here, first term, a= 10

Common difference, d = 20 - 10 = 10

490 = 10 + (n - 1)(10)

490 = 10 + 10n - 10

490 = 10n

n = 490/10

n = 49

If l is the last term of an AP, then the sum of the terms is given by

S = n/2[a+l]

So, S = 49/2[10 + 490]

= 49/2[500]

= 49(250)

= 12250

Therefore, the sum of the terms between 1 and 500 which are multiples of 2 as well as 5 is 12250.

✦ Try This: Find the sum of those integers between 500 and 900 which are multiples of 2 as well as of 5

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 2 (i)

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

Summary:

The sum of those integers between 1 and 500 which are multiples of 2 as well as of 5 is 12250

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