Question

Find the sum of all natural numbers not exceeding $1000$, which are divisible by $4$ but not by $8$.

• A. $62500$
• B. $62800$
• C. $64000$
• D. $65600$

Answer 1

Answer: (A)

$62500$

Natural Number divisible by $4$ but not $8$ are

$4,12,20,28,....996$

$996=4+(n-1)8$ ($n^{th}$ term formula)

$249=1+(n-1)2$ (divide both sides by 4)

$248=(n-1)2124+1=nn=125$

$S_n=4+12+20+......till125terms$

$S_n=4\left[\frac{n}{2}(2a+(n-1\left)d\right)\right]S_n=4\times \frac{125}{2}[2\times 1+124\times 2]S_n=250(2+248)S_n=62500$