What is an Arithmetic Progression?
An Arithmetic Progression (AP) or arithmetic series is a sequence of numbers such that the difference between any two consecutive numbers (or terms) is a constant value.
Examples:
Sequence 1 : 1, 2, 3, 4, 5, 6, ... Above sequence forms an AP since the difference between any two consecutive terms is same, which is equal to 1. See below:- 2 - 1 = 1 (2nd - 1st) 3 - 2 = 1 (3rd - 2nd) ... 6 - 5 = 1 (6th - 5th) Sequence 2 : -4, -2, 0, 2, 4, 6, ... Similarly above sequence also forms an AP:- (-2) - (-4) = 2 (2nd - 1st) (0) - (-2) = 2 (3rd - 2nd) ... 6 - 4 = 2 (6th - 5th) Sequence 3 : 1, 3, 5, 9, 4, 10, ... Above sequence doesn't form an AP as difference between any two consecutive terms is not same:- 3 - 1 = 2 5 - 3 = 2 9 - 5 = 4 4 - 9 = -5 10 - 4 = 6
Arithmetic Progression – Sum of First n Terms | Class 10 Maths
In Algebra a term is either a single number or variable or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by the divide.
Examples: In expression 5x – 10 = 1, 5x, 10 and 1 are the terms.