find the sum of all the multiples of 7 lying between 500 and 800.

The list of numbers between 500 and 800 that are multiples of 7 is :

504, 511, 518,.........................798.

Clearly the above list is in AP with first term, a = 504  and common difference, d = 7.

Let the n^th term of AP is 798.

 a_n = a + (n - 1)d

⇒ 798 = 504 + (n - 1)(7)

⇒ n = 43

sum of first 43 terms of the above AP is given by,