## Odd Number Formula

An odd number is always expressed either as 1 plus or minus an even number. Thus, the formula for odd numbers can be given as:

The Formula for identifying odd numbers is 2n ±1

A very easy method of finding weather the number is an odd number or not we can directly divide the number by 2 if after diving the number does not leave any remainder, we can say that it is even number and if the number leaves a remainder after the division, we can say that the number Is an odd number

Above we talked about finding the series of odd numbers using the odd number formula. We will further talk about finding the sum of odd number series by the formula of odd number so that the time of calculation decreases and become effective

The total Sum of first n odd numbers is said to be n2 where n denotes a natural number. For calculating the sum of odd numbers together we don’t add it one by one instead we use the formula of sum of odd numbers as it is easy to use and helps in getting the desired answer much faster than the other way.

### Solved Examples

**Q1:** Evaluate weather if 33 is an odd number by the help of odd numbers formula.

**Solution: **

To find: Checking weather 33 is an odd number.

After dividing 33 by 2, it leaves 1 as a remainder.

So we can say that 33 is an example of odd number.

**Final Answer:** It is an odd number.

**Q2:** By the help of odd number formula, find the solution for the following.

a) 1+ 3 + 5 + 7 +…….. 30 terms for the given equation. Find the sum of 30 terms where the next number is an odd number.

b) Find the total sum of all odd numbers from 1 to 31.

**Answer:**

a) N = 30. Accordingly, the sum = n2 = 302 = 900.

b) The required Sum = [(1+31)/2]2 = [32/2]2 =162 = 256