Question

Find the sum of all natural numbers between $100$ and $200$ which are divisible by $4.$

• A. $24552$
  
• B. $3600$
• C. $2357$
• D. $2112$

Answer 1

Answer: (B)

$3600$

The numbers between $100$ and $200$ which are divisible by $4$ are $104,108,112,...,196$.

This is an AP with first term $a=104$, common difference $d=4$ and last term $l=196$.

Let there be $n$ terms in this AP. Then,
$a_n=196\Rightarrow a+(n-1)d$

$196=104+(n-1)\times 4$

$\therefore n=24$
$\therefore$ Required sum $=S_n=\frac{n}{2}[a+l]=\frac{24}{2}[104+196]=3600$