Delhi Police Constable Exam Model Paper 10

Given:
The given series is $20+22+24+26+\dots \dots \dots .+60$
Formula:
Sum of first n even numbers $=\mathit{n}\left(\mathit{n}+1\right)$
Calculation:
$20+22+24+26+\dots \dots \dots \dots \dots .+60$
⇒ $\left(2+4+6+\dots \dots ..+60\right)\mathit{–}\left(2+4+6+\dots \dots \dots ..+18\right)$
⇒ $\left(30\times 31\right)\mathit{–}\left(9\times 10\right)$
⇒ $840$
Alternate Solution
Last term = First term + (n - 1) × Common difference
⇒ $60=20+{\left(\mathit{n}\mathit{–}1\right)}^2$
⇒ n = 21
Now, Sum of n terms in AP = $\frac{\mathit{n}}{2}\left(\mathit{a}+\mathit{l}\right)=\left(\frac{21}{2}\right)\times \left(20+60\right)=21\times 40=840.$