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Delhi Police Constable Exam Model Paper 2

Question : 80 of 100

Marks: +1, -0

Solution:

GIVEN:Numbers are from 11 to 120.

FORMULA USED:

Sum of first ‘n’ natural number =

\frac{n(n+1)}{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(120+1)}{2} - \frac{10(10+1)}{2}

7260 - 55

= 7205

Alternate Method

We know,

n^{\text{th}}

number =

1^{\text{st}}

number + (n - 1)d

⇒

120 = 11 + (n - 1) \times 1

⇒

109 = n - 1

⇒

n = 110

.Sum of n numbers,

S_n = \frac{n}{2} \times \left[2a + (n - 1)d\right] = \frac{110}{2} \times \left[2 \times 11 + (110 - 1) \times 1\right] = 55 \times (22 + 109) = 55 \times 131 = 7205

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