Find the sum of those integers from 1 to 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 from 1 to 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,.........,500.
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
500 = 10 + (n - 1)(10)
500 = 10 + 10n - 10
500 = 10n
n = 500/10
n = 50
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 = 50/2[10 + 500]
= 25[510]
= 12750
Therefore, the sum of the terms between 1 and 500 which are multiples of 2 as well as 5 is 12750.
✦ Try This: Find the sum of those integers from 500 to 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 (ii)
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5
Summary:
The sum of those integers from 1 to 500 which are multiples of 2 as well as of 5 is 12750
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