Question

Find the sum of all integers between 50 and 500, which are divisible by 7.

Answer 1

First number divisible by 7 in between 50 - 500 is 56

Last number divisible by 7 in between 50 - 500 is 497

Last term = 497 , first term = 56 , difference = 7 , so

497 = 56 + (n - 1)*d

497 - 56 = (n-1)*7

441 / 7 = (n - 1)

63 = n - 1

n = 64

So , there are 64 terms divisible in between 50 - 500 by 7

Now, applying the formula for additon

a = first term , l = last term

Sum = n / 2 [ a + l ]

= 64 / 2 [ 56 + 497 ]

= 17696

Ans: 17696