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The sum of the even numbers between 1 and 111 is:
Question

The sum of the even numbers between 1 and 111 is:

A.

3082

B.

3076

C.

3080

D.

3078

Correct option is C

Given:

Find the sum of even numbers between 1 and 111.

Formula Used:
Sum of n terms of an arithmetic progression (AP):

Sn=n2(a+l)S _n = \frac{n}{2} (a + l)​​

Number of terms:

n=lad+1n = \frac{l - a}{d} + 1

Solution:

n=11022+1=54+1=55 S=552(2+110)=552×112=55×56=3080n = \frac{110 - 2}{2} + 1 = 54 + 1 = 55 \\ \ \\S = \frac{55}{2} (2 + 110) = \frac{55}{2} \times 112 = 55 \times 56 = 3080

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