Arithmetic progression

Arithmetic progression as a sequence composed of real numbers links them together with a given pattern of the series. As a rule, the numerical series begins with the first term of the arithmetic progression as the starting point. Then each subsequent term of the progression is obtained by adding the same parameter, called the difference of arithmetic progression or step of arithmetic progression, to the previous one. If the difference is a positive number, then the entire sequence will tend towards positive infinity, as the values of the terms will increase as their ordinal numbers increase.

If the difference of the arithmetic progression is represented by a negative number, each subsequent term will be less than the previous one, and the entire sequence will tend towards negative infinity. In some cases, the limit of the arithmetic progression will be a specific number. This happens if the step of progression (difference) is equal to zero, then the first term of the arithmetic progression coincides with all the others.

Formulas of arithmetic progression include the following equalities:

• formula of the first term of arithmetic progression;

• formula nof the n-th term of progression;

• formula of the difference of arithmetic progression;

• formula of the sum of the first terms of arithmetic progression or the sum of a specific sample of terms.

According to all the formulas, the online calculator calculates the necessary values using the conditions under which the arithmetic progression is given. Numbers arranged in a symmetrical sequence allow you to calculate any term or sum of the progression, relying on just two or three parameters depending on the complexity level of the task.