Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

Here is a Solution ......

The positive integers, which are divisible by 5, are 5, 10, 15, ..., 1000

Out of these 10,20,30,.... 1000 are divisible by 2

Thus, we have to find the sum of the positive integers 5, 15, 25, ...., 995

If n is the number of terms in it the sequence then

995 = 5 + 10(n - 1) => 1000 = 10n

Therefore, n = 100.

Thus the sum of the series = (n/2)(a + l) = (100/2) (5 + 995) = 50000.