Formulas and properties of arithmetic progression

Arithmetic progression is a number sequence a1, a2, a3, ..., in which each term, starting from the second, equals the sum of the previous term and some constant number d, called the difference or step of the arithmetic progression.

n-th term of an arithmetic progression

an = a1 + (n - 1)d

an = an-1 + d

Difference of an arithmetic progression

d = an - an-1

Sum of the first n terms of an arithmetic progression

Sn = a1+an 2 ·n

Sn = 2a1+d(n-1) 2 ·n

Property of an arithmetic progression

an = an+1+an-1 2

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