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

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1 Answer

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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 = (n/2) x (a + l) 

= (250/2) x (2 + 500) 

= (250/2) x 502 

= 125 x 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) x (a + l) 

= (100/2) x (5 + 500) 

= 50 x 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 

Total numbers n = 500/10 = 50 

Now, Sum = (n/2) x (a + l) 

= (50/2) x (10 + 500) 

= 25 x 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

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