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Find the sum of even numbers between 1 and 25.

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155

156

157

158

answer is B.

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Detailed Solution

We need to find the sum of even numbers between 1 and 25.
The numbers are 2, 4, 6, 7, 8, .......... 24.

a = 2

d =

2

a_{n} = 24

The

n^{th}

term of an AP is calculated using

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

.
Substitute the values,

\Rightarrow 24 = 2 + (n - 1) 2

\Rightarrow 24 = 2 + 2 n - 2

\Rightarrow 24 - 2 + 2 = 2 n

\Rightarrow 24 = 2 n

\Rightarrow n = 12

The sum of the first

n

terms

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

S_{12} = \frac{12}{2} [2 \times 2 + (12 - 1) 2]

S_{12} = 6 [4 + (11) 2]

S_{12} = 6 [4 + 22]

S_{12} = 6 [26]

S_{12} = 156

Hence, the required sum is 156.
Therefore, option 2 is correct.

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