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Answers
Generally, two kinds of series are asked in the examination. One is based on numbers and the other based on alphabets.
In questions based on series, some numbers or alphabets are arranged in a particular sequence. You have to decipher that particular sequence of numbers or alphabets and on the basis of that deciphered sequence, find out the next number or alphabet of the series. Although there is no limit of logics which can be used to build a series, here are some important examples given which highlight the type of series asked in the examination.
How to solve number series problems:
Step 1: Observer are there any familiar numbers in the given series. Familiar numbers are primes numbers, perfect squares, cubes ... which are easy to identify.
Examples:
a. Prime number series: 2, 3, 5, 7, 11, 13, 17, . . .
b. Square series : 1, 4, 9, 16, 25, 36, 49, . . .
c. Cube series: 1, 8, 27, 64, 125, 216, 343, 512, 729, . . .
d. n2−1n2−1 series: 0, 3, 8, 15, 24,35, 48,
e. n2+nn2+n series: 2, 6, 12, 20, . . . .
Another Logic : The series is 1 x 2, 2 x 3, 3 x 4, 4 x 5, The next number is 5 x 6=30.
Step 2: Calculate the differences between the numbers. Observe the pattern in the differences. If the differences are growing rapidly it might be a square series, cube series, or multiplicative series. If the numbers are growing slowly it is an addition or subtraction series.
If the differences are not having any pattern then
1. It might be a double or triple series. Here every alternate number or every 3rd number form a series
2. It might be a sum or average series. Here sum of two consecutive numbers gives 3rd number. or average of first two numbers give next number
Example 1: 12, 9, 17, 13, 22, 17, 27, 21, 32, 25, 37, . . .
Answer: The above series is a mixed series. 12, 17, 22, 27, 32, 37, . . . form a series, 9, 13, 17, 21, 25, . . . form another series. So after 37 we get 29.
Example 2: 720, 120, 24, 6, ?
Answer: 720/6 = 120, 120/5 = 24, 24/4 = 6, 6/3 = 2