Question

Find the sum of even numbers between $11$ and $51$.

• A. $600$
• B. $610$
• C. $620$
• D. $630$

Answer 1

Answer: (C)

$620$

The sum of first n terms of arithmetic series formula can be written as,
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)
The list of even numbers between $11$ and $51$ is $12,14,16,18,.......50$
Where $n$ = number of terms
a = first even number $\Rightarrow$ 12
d = common difference of A.P. $\Rightarrow$ 2
$T_n=$ Last term $\Rightarrow$ 50
$T_n=a+(n-1)d$
$50=12+(n-1)2$
$50=12+2n-2$
$50-12+2=2n$
$40=2n$
$n=20$
Apply the given data in the formula (1),
$S_{20}=\frac{20}{2}[2\times 12+(20-1\left)2\right]$
$=10[24+(19\left)2\right]$
$=10[24+38]$
$=10\left[62\right]$
$=620$
So, the sum of even numbers between $11$ and $51$ is $620$.