Aptitude Odd Man Out and Series Concepts and Formulas

Points to Remember:

1. Series: The sequence of numbers that is obtained by some particular predefined rule is called series, and by applying this predefined rule it is possible to find out the next term of the series.

2. Arithmetic series: An arithmetic series is one in which successive numbers are obtained by adding (or subtracting) a fixed number to the previous number.

3. Geometric series: A geometric series is one in which each successive number is obtained by multiplying (or dividing) a fixed number by the previous number.

4. Series of squares, cubes, etc.: These series can be formed by squaring or cubing every successive number.

5. Mixed series: A mixed series means a series which is created according to any non-conventional rule.

1. Two-tier Arithmetic series: A two-tier arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series. For example, 2,5,10,17,26,37 is an example of two-tier arithmetic series. The difference of successive terms is 3,5,7,9,11..... which is an arithmetic series.
2. Three-tier Arithmetic series: In this series, the difference of successive numbers forms a two-tier arithmetic series, whose successive term's differences, in turn, create an arithmetic series. For example, 340, 214, 124, 64, 28, 10 ..... is an example of Three-tier Arithmetic Series. The differences of successive terms are 126, 90, 60, 36, 18,.... The differences of successive terms of this new series are 36, 30, 24, 18,..... which is an arithmetic series.
3. Arithmetic-Geometric series: In this series, each successive term should be found by first adding a fixed number to the previous term and then multiplying it by another fixed number. For example, 4,10,22,46..... is an example of arithmetico-geometric series in which each successive term is obtained by first adding 1 to the previous term and then multiplying it by 2.
4. Geometric-Arithmetic series: This series is one in which each successive term is found by first multiplying (or dividing) the previous term by a fixed number and then adding (or deducting) another fixed number. For example, 5, 11, 29, 83...... is a geometric-arithmetic series as in this series each successive term is obtained by first multiplying the previous number with 3 and then subtracting 4 from it.
5. Twin series: In twin series, two series are packed in one.

6. Some important steps to solve series questions:

• Do a preliminary screening of the series. If it is a simple series, it can be easily solved.
• If you fail in preliminary screening, determine the trend of the series, i.e., determine whether it is increasing, decreasing or alternating.
• (A) Perform this step only if a series is increasing or decreasing. Use the following rules:
  1. If the rise of a series is slow or gradual, the series is likely to have an addition-based increase, i.e., successive numbers are obtained by adding some numbers.
  2. If the rise of a series is very sharp initially but slows down later on, the series is likely to be formed by adding squared or cubed numbers.
  3. If the rise of a series is very sharp initially but slows down later on, the series is likely to be formed by adding squared or cubed numbers.
  4. If the rise of a series is throughout equally sharp, the series is likely to be multiplication based, i.e., successive terms are obtained by multiplying by some terms.
  5. If the rise of a series is irregular and haphazard, there may be two possibilities. Either there may be a mixture of two series or two different kinds of operations may be going on alternately.