Sunday, July 10, 2016

Arithmetic Progression

Definitions and Formulas

A collection of numbers arranged in a definite order according to some definite rule is called a sequence. e.g. 1,5,9,13,.....

If {tn} is a sequence then we denote the sum of first n terms of this sequence by Sn and formula is Sn = n(n+1)/2.

A special type of sequence in which the relationship between any two consecutive terms is the same is called a progression. e.g. 1,4,9,16,....

A sequence such that for a given first term, each term can be obtained by adding a fixed number to the preceding term is called an Arithmetic Progression. The fixed number is called common difference and is denoted by d. e.g. A.P. = a,a+d,a+2d,a+3d,....

Formula for general term : tn = a+(n-1)d.

Formula for sum of first n terms of an A.P. whose first term is a and the common difference is d is Sn = n/2 [ 2a+ (n-1)d].

For an A.P. whose first term is a and common difference is d, if any real number k is added to each term of the A.P. then the new sequence is also an A.P. with first term a+k and common difference d.