Question

Find the sum of even numbers between 1 and 25.

• A. $155$
• B. $156$
• C. $157$
• D. $158$

Answer 1

Answer: (B)

$156$

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 1 and 25 is 2, 4, 6, 7, 8, .......... 24
Where n = number of terms = ?
a = first even number

$a=2$
d = common difference of A.P.

$d=2$
$T_n=$ Last term

$T_n=24$
$T_n=a+(n-1)d$
$24=2+(n-1)2$
$24=2+2n-2$
$24-2+2=2n$
$24=2n$
$n=12$
Apply the given data in the formula (1),
$S_{12}=\frac{12}{2}[2\times 2+(12-1\left)2\right]$
$=6[4+(11\left)2\right]$
$=6[4+2]$
$=6\left[26\right]$
$=156$
So, the sum of even numbers between 1 and 25 is 156.