# What is the general formula of an arithmetic series?

## What is the general formula of an arithmetic series?

The sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). It is called the arithmetic series formula.

What are the two formulas of arithmetic series?

The sum of the terms of an arithmetic sequence is called an arithmetic series. We can write the sum of the first n terms of an arithmetic series as: Sn=a1+(a1+d)+(a1+2d)+……How To: Given terms of an arithmetic series, find the sum of the first n terms.

• Identify a1​ and an​.
• Determine n.

What is the formula of general sequence?

General Term Instead of y=mx+b, we write an=dn+c where d is the common difference and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by adding the common difference to the previous term is ak+1=ak+d.

### What is general formula in math?

The “General Form” of the equation of a straight line is: Ax + By + C = 0. A or B can be zero, but not both at the same time. The General Form is not always the most useful form, and you may prefer to use: The Slope-Intercept Form of the equation of a straight line: y = mx + b.

What is the example of formula?

A formula is an expression which calculates the value of a cell. For example, cell A3 below contains a formula which adds the value of cell A2 to the value of cell A1. For example, cell A3 below contains the SUM function which calculates the sum of the range A1:A2.

How to calculate an arithmetic series?

Here are the steps to follow for using this arithmetic series calculator: First, enter the value of the First Term of the Sequence (a1). Then enter the value of the Common Difference (d). Finally, enter the value of the Length of the Sequence (n).

#### How do you calculate the sum of a series?

To find the sum of a finite geometric series, use the formula, S n = a 1 ( 1 − r n ) 1 − r , r ≠ 1 , where n is the number of terms, a 1 is the first term and r is the common ratio .

How do you find the sum of the arithmetic sequence?

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a 1 and last term, a n, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n:

What is the formula for the arithmetic sequence?

An arithmetic sequence can be defined by an explicit formula in which an = d (n – 1) + c, where d is the common difference between consecutive terms, and c = a1. An arithmetic sequence can also be defined recursively by the formulas a1 = c, an+1 = an + d, in which d is again the common difference between consecutive terms, and c is a constant.