As we know, questions related to number series are very important in Quantitative aptitude section, So, today I'm going to discuss some problems of number series. These are just for your practice. I have already discussed this chapter in previous session i.e. Sequence and Series. Read this article first, then go through these examples.

## Examples with Solutions

**Example1:**In the following given series, find out the wrong number.

`1, 3, 10, 21, 64, 129, 356`

**Solution:**As i have discussed in previous session, operations applied on series can be: Addition or subtraction, multiplication or division, squaring or cubing and combination of any.

Series `1 3 10 21 64 129 356`

Difference ` 2 7 11 43 65 227`

By studying the above series, you'll come to know that, this is a combination of operations. Operation used is discussed as follows:

Alternately using: (`times 2 + 1`) and (`times 3 + 1`)

`1 times 2 + 1 = 3`

`3 times 3 + 1 = 10`

`10 times 2 + 1 = 21`

`21 times 3 + 1 = 64`

`64 times 2 + 1 = 129`

`129 times 3 + 1 = 388`

Therefore, last number of series is wrong i.e.`356`

**Example2:**Find the next number of the following series:

`672, 560, 448, 336, 224,?`

**Solution:**Check out the difference of each number first:

Series: `672 560 448 336 224`

Difference: `112 112 112 112`

Difference between all the terms is same i.e. `112`

Therefore, next term will be = `224 - 112` = `112` Ans

**Example3:**Find the next term of following series:

`82, 67, 54, 43, 34`

Solution: The operation used in series is discussed as follow:

`9^2 + 1` = `82`

`8^2 + 3` = `67`

`7^2 + 5` = `54`

`6^2 + 7` = `43`

`5^2 + 9` = `34`

Continuing like this;

`4^2 + 11` = `27`

Therefore, `27` is the next term.

**Example4:**What should come in place of question mark?

`1721, 2190, 2737, 3368,?`

**Solution:**As we can see, first term is approximately equal to the cube of `12`, so firstly we will try to solve it with the cubes.

`(12)^3 - 7` = `1721`

`(13)^3 - 7` = `2190`

`(14)^3 - 7` = `2737`

`(15)^3 - 7` = `3368`

Now you can find, that there is some pattern. So, continuing like this, we get

`(16)^3 - 7` = `4089` Ans

**Example5:**Find the next term of following series:

`8, 24, 12, 36, 18, ?`

**Solution:**Relation between the terms is as follows:

`8 times 3= 24`

`(24/2) = 12`

`12 times 3=36`

`(36)/2=18`

Continuing like this:

`18 times 3 = 54`

Therefore, next term is `54`

**Example 6:**Find the next term of the following series:

`47, 33, 21, 11, ?`

**Solution:**The pattern used in the series is as follows:

`7^2 - 2 = 47`

`6^2 - 3 = 33`

`5^2 - 4 = 21`

`4^2 - 5 = 11`

By continuing, we get

`3^2 - 6 = 3`

Therefore, `3` is the next term.

I will soon update the questions for your practice.

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