Number Series - Important Points
Different Types of Number Series
Series consisting of Perfect Squares
- 1, 4, 9, 16, 25, ...
- 2, 5, 10, 17, 26, ... (Perfect square + 1)
- 0, 3, 8, 15, 24, ... (Perfect square - 1)
- 441, 484, 529, 576, ...
Perfect Cube Series
- 1, 8, 27, 64, 125, ...
- 2, 9, 28, 65, 126, ... (Perfect cube + 1)
- 0, 7, 26, 63, 124, ... (Perfect cube - 1)
Arithmetic Series
It is a mathematical sequence there is a fixed difference between the numbers. The next terms are obtained either by adding a fixed number or by subtracting it.
The formula used to solve the number series problems is Xn = x1 + (n – 1)d
Examples:
- 2, 4, 6, 8, ...
- 1, 3, 5, 7, ...
- 11, 9, 7, 5, 3, ...
Geometric Series
It is a sequence in which each term of series is obtained by a fixed number multiplying or dividing the preceding number.
Examples:
- 3, 9, 27, 81, ...
- 2, 4, 8, 16, 32, ...
Arithmetico - Geometric Series
It is a peculiar combination of Arithmetic and Geometric series. An important property of this series is that in the Geometric Sequence there are differences of consecutive terms.
Example:
- 4, 18, 60, 186, ...
It follows the number series trick -
4, (4+2) x 3, (18+2) x 3, (60+2) x 3
Geometrico - Arithmetic Series
It is the reverse of Arithmetico –Geometric series. In this series, the suggestive terms differences are in the Arithmetic Series.
Example:
- 2, 7, 17, 37, 77, ...
It follows the number series trick -
2, (2x2) + 3, (7x2) + 3