Arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between any two consecutive terms is a constant value. This constant difference is called the common difference of the arithmetic progression. For example, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
The nth term of an arithmetic progression can be calculated using the formula an = a1 + (n-1)d, where a1 is the first term, d is the common difference, and n is the term number.
A finite portion of an arithmetic progression is called a finite arithmetic progression, and the sum of a finite arithmetic progression is called an arithmetic series. The formula for the sum of the first n terms of an arithmetic series is Sn = n/2.
In summary, an arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is a constant value, and the nth term and sum of the first n terms can be calculated using specific formulas.
