Question

The sum of the integers from 1 to 100 that are divisible by 2 or 5 is​

Answer 1

Answer:3050

Step-by-step explanation:Ths sum of arithmetric progression is

S = n 2 ( a + l )

, where  n  is the number of terms,  

a  is the first term and  

l  is the last term.

The sum of integres  1  to  100

which is divisible by  2is

S 2 = 2 + 4 + 6 + … 100 = 50 2 ⋅ ( 2 + 100 ) = 2550

and, the sum of integers divisible by  

5 is S 5 = 5+ 10 + 15 + … 100 = 20 2 ⋅ ( 5 + 100 ) = 1050

You may think the answer is  

S 2 + S 5 = 2550 + 1050 = 3600

but this is wrong.

2 + 4+ 6 + … 100  and  5 + 10+ 15 + … 100

have common terms.

They are integers divisible by  

10 , and their sum is

S 10 = 10 + 20 + 30 + … 100 = 10 2 ⋅ ( 10 + 100 ) = 550

Therefore, the answer for this question is  

S 2 + S 5 − S 10 = 2550 + 1050 − 550 = 3050