Question

find the sum of first 25 even numbers

Answer 1

Given:

First 25 even numbers.

To find:

The sum of the first 25 even numbers.

Solution:

The sum of the first 25 even numbers is 650.

To answer this question, we will follow the following steps:

The sequence of the first 25 even numbers is:

2, 4, 6, 8, till 25 even numbers.

( '0' is neither an even number nor an odd number)

This forms an arithmetic progression (A.P.) in which the sum of terms 'S' is given by:

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

where 'd' is a common difference, 'a' is the first term, n = number of terms till nth term.

So,

in the sequence 2, 4, 6, 8, till 25 even numbers.

a = 2, d = second term - first term = 4 - 2 = 2, n = 25

Now,

The sum of the first 25 even numbers is

$= \frac{25}{2} [2(2) + (25 - 1)2]$

$= \frac{25}{2} (4 + 48)$

$= \frac{25}{2} \times 52$

$= 25 \times 26$

$= 650$

Hence, the sum of the first 25 even numbers is 650.

Answer 2

Given,

The first 25 even numbers.

To find,

The sum of the first 25 even numbers.

Solution,

The sum of the first 25 even numbers will be 650.

We can easily solve this problem by following the given steps.

We know that even numbers are natural numbers that can be divided by 2. For example, 2,4,6, etc.

So, the series of the first 25 even numbers are:

2,4,6,8,---

Now, the difference between the two terms is common. So, it becomes an A.P.

The first term (a) = 2

Common difference(d) = second term - first term

d = 4-2

d = 2

The sum of all the terms in an A.P. = n/2 [2a+(n-1)d]

Sn = n/2 [2a+(n-1)d] where n is the number of terms.

S25 = 25/2 [ 2×2 + (25-1)2]

S25 = 25/2 [4+24×2]

S25 = 25/2 [4+48]

S25 = 25/2 (52)

S25 = (25×52)/2

S25 = 25×26

S25 = 650

Hence, the sum of the first 25 even numbers is 650.