Question

Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of S.

Answer 1

s= 325

Step by step explanation:

Add all numbers 1 to 25 to get 325.

Answer 2

325

Explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + 1

3 = 2 + 1

4 = 3 + 1

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

`sum = (n)/(2) \{ a + a _(n) \}`

here,

• n is the number of terms
• a is the first number of the series
• an is the last number of the series

So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

`S = (25)/(2)\{ 1 +25\}`

`= (25 * 26)/(2)`

`= 25 * 13`

`= 325`

So, the value of S comes out to be 325.