Question

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

• A. $10050$
• B. $5050$
• C. $5000$
• D. $50000$

Answer 1

The correct option is D $50000$

The positive integer which are divisible by $5$ are $5,10,15,\mathrm{20........1000}$, out of these $10,20,\mathrm{30..............1000}$ are divisible by $2$.

Thus, we have to find the sum of positive inters $5,15,\mathrm{25.....995}$

If $n$ is the number of terms in it, the sequence is

$995=5+10(n-1)$

$\Rightarrow 1000=10n$

$\Rightarrow n=100$

Thus, the sum of numbers $=$ $\frac{100}{2}[5+995]=\left(50\right)\left(1000\right)=50000$