What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?

Solution (By Examveda Team)

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
∴ n = 100
Thus the sum of the series
$$\eqalign{ & = \left( {\frac{n}{2}} \right)\left( {a + l} \right) \cr & = \left( {\frac{{100}}{2}} \right)\left( {5 + 995} \right) \cr & = \frac{{100 \times 1000}}{2} \cr & = 50000 \cr} $$