Question

find the sum of integers from 1 to 500 which are multiples of 2 or 5

Answer 1

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

this is your answer


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