Arithmetic Progressions Class 10th Formulas

CBSE Arithmetic Progressions Class 10th Formulas


Sequence:  A sequence is arrangement of numbers in a definite order and are formed according to some definite rule.

For example:

Term of a sequence : 

Arithmetic Progression (AP):  An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number (d) to the preceding term, except the first term (a). The fixed number d is called common difference.The  general form of an AP is a, a + d, a + 2d,a + 3d,…

Common difference :  

General term/nth term of an AP :  

nth term from the end of an AP : If l is the last term of an AP whose common difference is d. Then nth term from end is l – (n-1)d.

Finite and infinite sequence : If the last term of the sequence is known or can be known then the sequence is called finite sequence.

For example : (i) 4,8,11,14,…,302  and -20, -18, -12,…,88 are infinite sequences.

(ii) -3, 1, 5, 9, … and 7, 14, 28,42,56, … are infinite sequences.

Sum of  first n terms of an AP :