What is an arithmetic progression?
Answer
An arithmetic progression is a sequence in which each term differs from the previous one by a fixed constant called the common difference.
The working
Definition
In an AP, the difference between any two consecutive terms is constant. This constant is called the common difference, d.
General form
An AP is written as a, a + d, a + 2d, a + 3d, and so on, where a is the first term and d is the common difference.
nth term
The nth term is aₙ = a + (n − 1)d. For example, the 5th term of 3, 7, 11, ... is 3 + 4 × 4 = 19.
Sum of n terms
The sum of the first n terms is Sₙ = (n÷2)[2a + (n − 1)d], which also equals (n÷2)(first term + last term).
Example
The sequence 2, 5, 8, 11, ... is an AP with a = 2 and d = 3.
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