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Arithmetic Progression

Sequences: Sequences are a set of numbers, which are arranged according to any specific rule. There is no exception for any type of numbers, any type of rules according to which they are arranged. The set of numbers should have a definite, logical rule according to which they are arranged. It need not be a mathematical formula, but it should be logical. Such a set of numbers are called a sequence of numbers.

For example, the following is a sequence of numbers, because they are arranged according to a definite rule:

• {2, 4, 6, 8, 10, 12} Rule: nth term = 2n
• {3, 5, 7, 9, 11, 13} Rule: nth term = 2n + 1
• {2, 3, 5, 7, 11, 13, 17} Rule: Prime numbers

Progressions: Progressions are yet another type of number sets which are arranged according to some definite rule. The difference between a progression and a sequence is that a progression has a specific formula to calculate its nth term, whereas a sequence can be based on a logical rule like 'a group of prime numbers', which does not have a formula associated with it.

Co-ordinate Geometry

Cartesian coordinates of the plane

The Cartesian coordinates in the plane are specified in terms of the x coordinates axis and the y-coordinate axis, as illustrated in the below figure. The origin is the intersection of the x and y-axes. The Cartesian coordinates of a point in the plane are written as (x,y). The first number x is called the x-coordinate (or abscissa), as it is the signed distance from the origin in the direction along the x-axis. The x-coordinate specifies the distance to the right (if x is positive) or to the left (if x is negative) of the y-axis. Similarly, the second number y is called the y-coordinate (or ordinate), as it is the signed distance from the origin in the direction along the y-axis, the y-coordinate specifies the distance above (if y is positive) or below (if y is negative) the x-axis.

Quadrant: The Cartesian plane is divided into four quadrants. These are numbered from I through IV, starting with the upper right and going around counter clockwise.