Odd Number Series

Introduction to odd number series:

Odd Number definition: A number ‘x’ which is not divided exactly by 2 then ‘x’ is odd number. For example 3 is odd number which is not divided exactly by 2. If it is divided by 2 then ‘x’ is even number. In another way we can find the odd number easily. Whether the last digit of number ends with 1, 3, 5, 7 and 9 then we can say that as odd number.

For example:  87 are odd or even?

The number end with 7 so according to our definition 87 is odd.

We write the odd number series from 1 to 100 as

1, 3, 5, 7 ... up to 99.
1 + 3 + 5 + 7 + … + 99
To find the nth term of number series formula is

tn = a + (n – 1)d

To find the sum of an number series formula is

Sn = n/2 [ 2a + (n – 1)d ]

Or

Sn = n/2 [ a + l ]

Here ‘n’ is number of term

‘a’ is first term of series

‘d’ is difference between two consecutive terms

‘l’ is Last term of the series

Example: 1 + 3 + 5 + … find 13th term of this series?

Solution:

a = 1;

d = 2nd term – first term = 3 – 1 = 2

n = 13

tn = a + (n – 1)d

= 1 + (13 – 1)2

= 1 + (12)2

= 1 + 24

= 25

t13 = 25

Example Problem on Odd Number Series

Find Sum of first three odd numbers?
Solution:

Let us take first three odd number is 1, 3, and 5.

Sum of three odd number = 1 + 3 + 5

= 9

List out odd numbers greater than 2 and smaller than 20.
Solution:

Which is not divisible by 2 then the number is called odd number.

Odd numbers = 3, 5, 7, 9, 11, 13, 15, 17 and 19.

8 odd numbers available in between the greater than 2 and smaller than 20.

Prove that sum of an even number and odd number as odd number?
Proof:

Let us take ‘2x’ is Even number and ‘2y + 1’ Odd number.

Sum of these even and odd numbers:

2x + (2y +1) = 2(x + y) + 1

Let N = x + y and we can write the sum as

2x + (2y +1) = 2N +1

Let,

x =1 then 2x = 2; y = 2 then 2y + 1 = 5;

2x + 2y + 1 = 2(1 + 2) +1

= 6 + 1

= 7 this is odd number.

Therefore “sum of an even and odd number is odd number”

Sum of three consecutive odd numbers are 21 then find their odd numbers?
Solution:

Let us take 2x + 1 is one odd number

Then consecutive three odd numbers = 2x + 1, 2x + 3, 2x + 5

Sum of these odd numbers = 21

2x + 1+ 2x + 3+ 2x + 5 = 21

6x + 9 = 21

6x = 12

x = 12 / 6

x = 2

Then    2x + 1 = 2 (2) + 1 = 5

2x + 3 = 2 (2) + 3 = 7

2x + 5 = 2 (2) + 5 = 9

The odd numbers are 5, 7, and 9.

3, 7, 11, … find the sum upto 15th term?
Solution:

a = 3; d = 7 – 3 = 4; n = 15

Formula is,

Sn = n/2 [ 2a + (n – 1)d ]

= 15/2 [2*3 + (15 – 1)*4]

= 15/2 [6 + 56]

= 15/2 [62]

S15 = 465

Between, if you have problem on these topics Even Number, please browse expert math related websites for more help on Convert Fraction to Percent.

Exercise on Odd Number Series

Practice problem on odd number series

The sum of two odd consecutive numbers is 16. Find their odd numbers?
Sum of two odd numbers is _______?
The sum of four odd numbers is 40. The three odd numbers is 9, 11 and 13 find the 4th odd number?
1 + 7 + 13 +…. Find the 20th term?
1 + 5 + 9 +….  Find sum up to 18th term?
Answer Key of odd number series

7, 9
Odd
7
115
630