Perfect Square Series: This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.
Example 1: 841, ?, 2401, 3481, 4761
Solution:

[latex]29^{2}[/latex], [latex]39^{2}[/latex], [latex]49^{2}[/latex], [latex]59^{2}[/latex], [latex]69^{2}[/latex]

Example 2: 1, 9, 25, ?, 81, 121
Solution:

[latex]1^{2}[/latex], [latex]3^{2}[/latex], [latex]5^{2}[/latex], [latex]7^{2}[/latex], [latex]9^{2}[/latex], [latex]11^{2}[/latex]

Example 3: 289, 225, 169, ?, 81
Solution:

[latex]17^{2}[/latex], [latex]15^{2}[/latex], [latex]13^{2}[/latex], [latex]11^{2}[/latex], [latex]9^{2}[/latex]

Perfect Cube Series: This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series.
Example 1: 3375, ?, 24389, 46656, 79507
Solution:

[latex]15^{3}[/latex], [latex]22^{3}[/latex], [latex]29^{3}[/latex], [latex]36^{3}[/latex], [latex]43^{3}[/latex]
(Each cube digit added with seven to become next cube number)

Example 2: 729, 6859, 24389, ?, 117649, 205379
Solution:

[latex]9^{3}[/latex], [latex]19^{3}[/latex], [latex]29^{3}[/latex], [latex]39^{3}[/latex], [latex]49^{3}[/latex], [latex]59^{3}[/latex]

Example 3: 1000, 8000, 27000, 64000, ?
Solution:

[latex]10^{3}[/latex], [latex]20^{3}[/latex], [latex]30^{3}[/latex], [latex]40^{3}[/latex], [latex]50^{3}[/latex]

Ration Series: This type of series are based on ration series, where sequence are in form of ratio in difference between the numbers. All numbers are arranged in ratio sequence order.
Example 1: 11, 22, 44, 88, ?
Solution:

Separate each number and
= 11 x 2 = 22,
= 22 x 2 = 44,
= 44 x 2 = 88,
= 88 x 2 = 176.

Example 2: 13, 26, 412, ?, 1648
Solution:

Separate each number and
= (1+1 = 2, 3+3 = 6) = 26,
= (2+2=4, 6+6 = 12) = 412,
= (41+41=82, 2+2=4 = 824,
= (82+82=164,4+4= 8)=1648.
So, the missing term is 824.

Geometric Series: This type of series are based on ascending or descending sequence of numbers and each continuous number is obtain by multiplying or dividing the preceding number with static number.
Example 1: 3, ?, 45, 144, 585
Solution:

3 x 0 +9 = 9, 9 x 1 + 9 = 18, 18 x 2 + 9 = 45, 45 x 3 + 9 = 144, 144 x 4 + 9 = 585.

Example 2: 5, 45, 405, 3645, ?
Solution:

5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

Example 3: 73205, 6655, 605, 55, ?
Solution:

5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205.

Two stage Type Series: A two stage Arithmetic series is one in which the formation of arithmetic series are obtain from differences of continuous numbers themselves.
Example: 1, 3, 6, 10, 15.....
Solution:

3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, 15 - 10 = 5....
Now, we get an arithmetic sequence 2, 3, 4, 5

Mixed Series: This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.
Example: 11, 24, 50, 102, 206, ?
Solution:

11 x 2 = 22 +2 = 24,
24 x 2 = 48 + 2 = 50,
50 x 2 = 100 + 2 = 102,
102 x 2 = 204 + 2 = 206,
206 x 2 = 412 + 2 = 414.
So the missing number is 414.

1. Find out the series 291, 304, 317, ?, 343
Solution:

Given series 291, 304, 317, ?, 343
First, find the common difference between the numbers
i.e. 304 - 291 = 13
317 - 304 = 13
Now, just add 13 to 317
⇒ 317 + 13 = 330
Therefore series is 291, 304, 317, 330, 343

2. Find out the series 9, 18, 36, 72, ?
Solution:

Given series is 9, 18, 36, 72, ?
Notice that every number is a multiple of 2 i.e.
9 × 2 = 18
18 × 2 = 36
36 × 2 = 72
72 × 2 = 144
Therefore, the series is 9, 18, 36, 72, 144

3. Find out the series 30, 45, 75, 120, 180, 255, ?
Solution:

Given series 30, 45, 75, 120, 180, 255, ?
First, find out the common difference between the numbers i.e.
45 - 30 = 15
75 - 45 = 30
120 - 75 = 45
180 - 120 = 60
255 - 180 = 75
Now see the pattern of common difference i.e.
15 × 1 = 15
15 × 2 = 30
15 × 3 = 45
15 × 4 = 60
15 × 5 = 75
15 × 6 + 255 = 345
Therefore, the series is 30, 45, 75, 120, 180, 255, 345

4. Find out the series 9, 90, 154, 203, 239, 264, ?
Solution:

Given series 9, 90, 154, 203, 239, 264, ?
Multiply second last number by 2 i.e. 2 × 239=478 > 264
So, take common difference between them
90 - 9 = 81
154 - 90 = 64
203 - 154 = 49
239 - 203 = 36
264 - 239 = 25
By observing the above pattern, they are square numbers i.e [latex]9^2, 8^2, 7^2, 6^2, 5^2, 4^2[/latex] respectively
So, [latex]4^2[/latex] + 264 = 280
Therefore, series is 9, 90, 154, 203, 239, 264, 280

5. Find out the series 7, 13, 25, 49, 97, 194, 385?
Solution:

Given series 7, 13, 25, 49, 97, 194, 385?
7 × 2 - 1 = 13
So, 13 × 2 - 1 = 25
25 × 2 - 1 = 49
49 × 2 - 1 = 97
97 × 2 - 1 = 193
193 × 2 - 1 = 385
Therefore, the wrong number is 194