Number System Practice Test 5

The sum of first n terms of arithmetic series formula can be written as,
${\mathit{S}}_{\mathit{n}}=\frac{\mathit{n}}{2}\left[2\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}\right]$
The list of even numbers between 1 and 50 is $2,4,6,7,8,$ , .......... 50
Where $\mathit{n}=$ number of terms $=?$
$\mathit{a}=$ first even number $\Rightarrow 2$ $\mathit{d}=$ common difference of A.P. $\Rightarrow 2$
${\mathit{T}}_{\mathit{n}}=$ Last term $\Rightarrow 50$
${\mathit{T}}_{\mathit{n}}=\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}$
$50=2+\left(\mathit{n}-1\right)2$
$50=2+2\mathit{n}-2$
$50-2+2=2\mathit{n}$
$50=2\mathit{n}$
$\mathit{n}=25$
Apply the given data in the formula (1),
${\mathit{S}}_{25}=\frac{25}{2}\left[2\times 2+\left(25-1\right)2\right]$
$=\frac{25}{2}\left[4+\left(24\right)2\right]$
$=\frac{25}{2}\left[4+48\right]$
$=\frac{25}{2}\left[52\right]$
$=25\times 26$
$=650$

The sum of even numbers from 1 to 50 is $650$