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Clearly, it is an Arithmetic Progression whose first term = 1, last term = 25 and number
of terms = 25.

Therefore, S = (25 + 1), [Using the formula S = (a + l)]

= (26)

= 25 × 13

= 325

Therefore, the sum of first 25 natural numbers is 325.

Example 2- Find the sum of the following Arithmetic series:

1 + 8 + 15 + 22 + 29 + 36 + ………………… to 17 terms

Solution- First term of the given arithmetic series = 1

Second term of the given arithmetic series = 8

Third term of the given arithmetic series = 15

Fourth term of the given arithmetic series = 22

Fifth term of the given arithmetic series = 29

Now, Second term - First term = 8 - 1 = 7

Third term - Second term = 15 - 8 = 7

Fourth term - Third term = 22 - 15 = 7

Therefore, common difference of the given arithmetic series is 7.

The number of terms of the given A. P. series (n) = 17

We know that the sum of first n terms of the Arithmetic Progress, whose first term = a
and common difference = d is

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