# Series Completion

In series completion some numbers, which are following some particular pattern are given and we are ask to find the no missing in the given series.
Some rules used in such problems are as follows:
Rule-1
Add or subtract or multiply or divide by certain no in order to get next no.
Example: 8, 12, 16, ___, 24, 28.
Explanation: Here next no can be achieved by simply add 4 to the previous no.Hence the missing no would be 20.

Rule-2
Apply the below given mathematical combinations in order to get the next no.

 Addition & Subtraction Minus & Multiplication Multiplication & Division Division & Addition

Example: 15, 10, 5, 150, 16, 12, 4, 192, 20, 15, 5, ____
Explanation: Here the 3rd no can be achieved by subtracting the 2nd no from 1st while the 4th no is achieved by multiplying the 1st and 2nd and so on. Therefore the combination used here is Subtraction & multiplication. Hence by this combination the missing no would be 300.

Rule-3
Multiplication of any number of series.
Example: 3, 10, 33, 104, _____
Explanation: Here the pattern followed is as per
3*3+1     =10
10*3+3   =33
33*3+5   =104
104*3+7 =319

Rule-4
Squares (or) Cubes
Example: 2, 12, 56, 182, 462,____
Explanation:
2=12 +1
12= 32 +3
56= 72 +7
182=132 +13
462=212 + 21
The series formed by subtracting the consecutive no after splitting into square form is
3-1=2
7-3=4
13-7=6
21-13=8
X - 21 =10 , Thus X= 31 and hence the missing no= 312 +31= 992