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Number System Practice Test 5

Question : 5 of 40

Marks: +1, -0

Find the sum of all even numbers between 1 to 50.

Solution:

The sum of first n terms of arithmetic series formula can be written as,

S_{n}=\;\frac{n}{2}\left[2a+(n-1)d\right]

The list of even numbers between 1 and 50 is

2,4,6,7,8,

, .......... 50

Where

n=

number of terms

=?

a=

first even number

\Rightarrow 2

d=

common difference of A.P.

\Rightarrow 2

T_{n}=

Last term

\Rightarrow 50

T_{n}=a+(n-1)d

50=2+(n-1)2

50=2+2n-2

50-2+2=2n

50=2n

n=25

Apply the given data in the formula (1),

S_{25}=\;\frac{25}{2}\left[2 \times 2+(25-1)2\right]

=\frac{25}{2}\left[4+(24)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

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