Delhi Police Constable Exam Model Paper 2

GIVEN:Numbers are from 11 to 120.
FORMULA USED:
Sum of first ‘n’ natural number = $\frac{\mathit{n}\left(\mathit{n}+1\right)}{2}$
CALCULATION:
Sum of all numbers from 11 to 120 = Sum of first 120 natural numbers – Sum of first 10 natural numbers.
Sum of all numbers from 11 to 120 = $\frac{120\left(120+1\right)}{2}-\frac{10\left(10+1\right)}{2}$
= $7260\mathit{–}55$
= 7205
Alternate Method
We know, ${\mathit{n}}^{\mathit{t}\mathit{h}}$ number = $1^{\mathit{s}\mathit{t}}$ number + (n - 1)d
⇒ $120=11+\left(\mathit{n}-1\right)\times 1$
⇒ $109=\mathit{n}-1$
⇒ $\mathit{n}=110$
.Sum of n numbers, ${\mathit{S}}_{\mathit{n}}=\frac{\mathit{n}}{2}\times \left[2\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}\right]=\left(\frac{110}{2}\right)\times \left[2\times 11+\left(110-1\right)\times 1\right]=55\times \left(22+109\right)=55\times 131=7205$