Sequence and Series
To crack any question of series, try the following tricks in the same order as mentioned below â€“
 Squares/Cubes: First of all try to see whether the series has been made from the squares/cubes of natural numbers. Most of the time series is made by adding or subtracting a fix value from the squares/cubes of natural numbers.
For Example
Find the next term in the series 2, 9, 28, 65, ?
In this example, each term has been constructed by adding 1 to the cubes of natural number starting with 1. ie. we can write the above series as (1^{3} + 1), (2^{3} + 1), (3^{3} + 1), (4^{3} + 1), hence the next term should be (5^{3} + 1) or 126.
 Arithmetic/Geometric Progression: Next you, have to see if the series is an arithmetic progression or a geometric progression. In many case it will be.
For Example
4, 11, 18, 25 is an AP, in which, each new term has been formed by adding 7 to previous term. So, in this case next term will be 32.
Similarly, 6, 36, 216, 1296 is an GP which has been created by multiplying 6 to each term. Next term in this case will be 7776.
 Mix of AP/GP: Many times, series are formed by combining AP and GP together. For example, let find the next term of the following series â€“ 2, 4, 12, 48, ?
 Finding Answer by taking the difference up to two levels: Most of the series questions which do not fall under above categories, can be solved by taking the difference of each term up to 2 levels.
Example3, 6, 11, 18, 27, ?SolutionWhen we subtract the numbers of the series for the first time, then we get 3 (6  3), 5 (11  6), 7 (18  11), 9 (27  18), So, the next term will be 38 (38  27 = 11)..

Miscellaneous Series:
 Find the next term in the series â€“ 2, 3, 5, 7, 11, 13, ?
 Find the next term in the series â€“ 77, 49, 36, 18, ?
 Find the next term in the series â€“ 2, 5, 7, 12, 19, 31, ?
 Find the next term of the series â€“ 3, 4, 12, 48, ?
 Find the next term in the series â€“ 2, 3, 5, 7, 11, 13, ?