Question

Find the sum of those integers from 1 to 500 which are multiples of 2or 5​

Answer 1

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

Total numbers n = 500/2 = 250

Now, Sum = (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

Total numbers n = 500/5 = 100

Now, Sum = (n/2)*(a + l)

= (100/2)*(5 + 500) = 50 * 505 = 25250

, 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

Total 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