What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?
A. 10,050 B. 5050 C. 5000 D. 50,000 Answer: Option DShow Answer
Solution(By Apex 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
$\begin{aligned}&=\left(\frac{n}{2}\right)(a+l)\\
&=\left(\frac{100}{2}\right)(5+995)\\
&=\frac{100\times1000}{2}\\
&=50000\end{aligned}$
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