Question

What is the sum of all even numbers between $500$ & $600$ ?

• A. $26950$
• B. $27500$
• C. $27950$
• D. $26500$

Answer 1

The correct option is A $26950$

Sum of all even numbers between $500$ and $600$

Even numbers between $500$ and $600$

$\Rightarrow 502,504,\dots .598$

It is an $AP$ with $a=502$

And $d=2$

$a_n=a+(n-1)d$

$598=502+(n-1)2$

$\Rightarrow (n-1)=\frac{598-502}{2}$

$\Rightarrow n=1+\frac{96}{2}\Rightarrow 49$

Sum of $n$ terms $=\frac{n}{2}[2a+(n-1)d]$

$=\frac{49}{2}[2\left(502\right)+\left(48\right)2]$

$=49[\left(502\right)+48]$

$=550\times 49$

$=26950$

$\therefore$ sum of even numbers between $500$ and $600$ is $26950$