Tricks to solve problems related to Series in Quantitative Aptitude Today, I'm going to discuss a very important topic of Quantitative aptitude i.e. Sequence and Series. Sequence and Series is a mathematical concept and basically it is a logical concept.

Sequence and Series

Problems with sequence and series simply follow a specific pattern. Most quantitative aptitude tests typically include questions about series completion. To finish the series, you simply need to understand the set relationship. You can figure out the solution once you recognize the series' pattern.
Remember, Study the set relationship first
When there are four or five options presented for a question on a quantitative aptitude test, try to eliminate them in order to make the question easier. This will help you to save your precious time. Coming to the point, I'm going to discuss some standard patterns of series. Go through these rules and try to solve the problems related to this.Some standard patterns of series

Addition or Subtraction

In order to determine the following term, a number (or pattern of numbers) may be added or subtracted during each term.
Example1: Study the following series and try to find the next term,
3, 6, 9,12,15, ?
Solution: This is very simple pattern. You can easily find that 3 is added to each term , and we are getting next term.
$3+3=6$

$6+3=9$

$9+3=12$

Similarly, $15+3=18.$

So, 18 will the next term. 
Example2: Complete the following series
4, 6, 9, 13, 18,?
Solution: Pattern used in series:
$4+2=6$

$6+3=9$

$9+4=13$

$13+5=18$

Therefore,

$18+6=24$.

So, 24 will be next term.
Example3: Study one more term and find the next term of series.
13, 11, 9, 7, 5, ?
Solution: As this is decreasing pattern, you can easily find that 2 is subtracted from each term to get the next term.
$13-2=11$

$11-2=9$

$9-2=7$

Similarly, $5-2=3.$

So, 3 will be  the last term.

Multiplication or Division

Another pattern may be related to multiplication or division of some number to each term to get the next term.
Example4: Study the pattern of series and try to find next term
4, 8, 24, 96,?
Solution: A particular pattern of numbers is multiplied to each term of series
$4\times 2=8$

$8\times 3=24$

$24\times 4=96$

So, $96\times 5=480$.

480 will be the last term.
Example5: Complete the following series
480, 96, 24, 8,?
Solution: Study the pattern and note that it is a decreasing pattern and a particular series of number is divided from previous term
$\frac{480}{5}=96$

$\frac{96}{4}=24$

$\frac{24}{3}=8$

Continuing, $\frac{8}{2}=4.$

Therefore, 4 will be the next term.

Squaring or cubing

Another rules may be of squaring or cubing of the terms of series.
Example6: Complete the following series
4,9,16,25,?
Solution: This is a very simple pattern i.e. a square of some pattern of numbers
$2^2=4$

$3^2=9$

$4^2=16$

$5^2=25$

Continuing, $6^2=36$.

36 is the next term.
Example7: Study the following series and try to complete
1, 27, 125, 343,?
Solution: The series is based on following pattern:
$1^3=1$

$3^3=27$

$5^3=125$

$7^3=343$

Continuing, $9^3=729,$

So, 729 will be the next term.

Mixed Patterns

Some questions employ a combination of the patterns mentioned above. For instance, one value is multiplied by the series' first term, while another is removed to obtain the series' second term. To help you understand, I'll use some examples. Try to figure it out on your own first.
Example8: Try to find the next term of following series:
1, 2, 6, 21, 88,?
Solution: Study this series, you will find out that more than one rule is applied on it. Following pattern is used in it:
$1\times 1+1=2$

$2\times 2+2=6$

$6\times 3+3=21$

$21\times 4+4=88$

Series (1, 2, 3....) multiplied to term and then same series is added to get the next term Therefore,

$88\times 5+5=445.$

445 is the next term.
Example9: Find the next term of following series:
276, 140, 68, 36,?
Solution: Following pattern is used in the series:
$\frac{276}{2}+2=140$

(Term is divided by 2 then added by 2)

$\frac{140}{2}-2=68$

(Term is divided by2 then subtracted by 2)

$\frac{68}{2}+2=36$ 

Therefore, each term is divided by 2 then alternately added and subtracted by 2 to get the next term.

So $\frac{36}{2}-2=16$.

16 is the next term.
Thus, there are large number of techniques to form number of series. The only thing is the pattern of the series.