Given an AP is required of all integers between 50 and 500, which are multiples of 7
To find : the sum of all integers between 50 and 500 which are divisible by 7
So, the sequence is 56, 63, 70….497
It is an AP whose first term is 56 and d is 7
Hence,
The sum is given by the formula s = \(\frac{n}{2}\)(2a + (n-1)d)
Now,
For the finding number of terms, the formula is
n = 64
Substituting n is the sum formula we get,
s = \(\frac{64}{2}\)(2 x 56 + (63) x 7)
s = 17696