Find the sum of those integers between 1to500 which are multiples of 2 as well as of 5
Answers
Step-by-step explanation:
The numbers from 1 to 500 which are multiple of 2 are:
2, 4, 6, 8.............500
This forms an AP, where
first term a = 2,
common difference = 4 - 2 = 2
last term l = 500
Toral numbers n = 500/2 = 250
Now, Sum = (n/2)*(a + l)
= (250/2)*(2 + 500)
= (250/2) * 502
= 125 * 502
= 62750
The numbers from 1 to 500 which are multiple of 5 are:
5, 10, 15, 20.............500
This forms an AP, where
first term a = 5,
common difference = 10 - 5 = 5
last term l = 500
Toral numbers n = 500/5 = 100
Now, Sum = (n/2)*(a + l)
= (100/2)*(5 + 500)
= 50 * 505
= 25250
Again, multiple of 10 are included in both i.e. in multiple of 2 and multiple of 5 also.
Now, the numbers from 1 to 500 which are multiple of 10 are:
10, 20, 30.............500
This forms an AP, where
first term a = 10,
common difference = 20 - 10 = 10
last term l = 500
Toral numbers n = 500/10 = 50
Now, Sum = (n/2)*(a + l)
= (50/2)*(10 + 500)
= 25 * 510
= 12750
Now, the sum of integers from 1 to 500 which are multiple of 2 or 5 = sum of multiple of 2 + sum of multiple of 5 - sum of multiple of 2 and 5
= 62750 + 25250 - 12750
= 88000 - 12750
= 75250
The numbers from 1 to 500 which are multiple of 2 are:
2, 4, 6, 8.............500
This forms an AP, where
first term a = 2,
common difference = 4 - 2 = 2
last term l = 500
Toral numbers n = 500/2 = 250
Now, Sum = (n/2)*(a + l)
= (250/2)*(2 + 500)
= (250/2) * 502
= 125 * 502
= 62750
The numbers from 1 to 500 which are multiple of 5 are:
5, 10, 15, 20.............500
This forms an AP, where
first term a = 5,
common difference = 10 - 5 = 5
last term l = 500
Toral numbers n = 500/5 = 100
Now, Sum = (n/2)*(a + l)
= (100/2)*(5 + 500)
= 50 * 505
= 25250
Again, multiple of 10 are included in both i.e. in multiple of 2 and multiple of 5 also.
Now, the numbers from 1 to 500 which are multiple of 10 are:
10, 20, 30.............500
This forms an AP, where
first term a = 10,
common difference = 20 - 10 = 10
last term l = 500
Toral numbers n = 500/10 = 50
Now, Sum = (n/2)*(a + l)
= (50/2)*(10 + 500)
= 25 * 510
= 12750
Now, the sum of integers from 1 to 500 which are multiple of 2 or 5 = sum of multiple of 2 + sum of multiple of 5 - sum of multiple of 2 and 5
= 62750 + 25250 - 12750
= 88000 - 12750
= 75250