Q:

How do you calculate the sum of an arithmetic sequence?

A:

Calculate the sum of an arithmetic sequence with the formula (n/2)(2a + (n-1)d). The sum is represented by the Greek letter sigma, while the variable a is the first value of the sequence, d is the difference between values in the sequence, and n is the number of terms in the series.

Keep Learning

Credit: Image Source Vetta Getty Images

1. Determine the difference between terms

Find the arithmetic value that describes the difference between each term in the series, and set it equal to d. For example, the series {1, 2, 3} has a difference of 1 between each term, while the series {0, 3, 6, 9} has a difference of 3.

2. Find the number of terms in the series

The number of terms added together in the series is represented by the variable n, so count up the total number of terms you want to find the sum of. For example, the series {2, 4, 6, 8} has four terms, so the value of n would be 4.

3. Plug the numbers into the equation

Using the equation (n/2)(2a + (n-1)d), plug in the found values for the variables n, a and d.

4. Calculate the equation

With all of the values entered, use basic arithmetic to calculate the total sum.

Sources:

Related Questions

• A: A recursive sequence is an ordered set of numbers where the first items are called starting values and all other terms can be computed recursively from the... Full Answer >
Filed Under:
• A: The next number in this sequence is 24. This would follow the pattern of adding five to a number and then subtracting two. The first three numbers of this ... Full Answer >
Filed Under:
• A: In math, the term n of a sequence refers to the algebraic representation of any given term in the sequence. This contrasts with the specific values of name... Full Answer >
Filed Under:
• A: The associative property of multiplication states that the order in which numbers are multiplied in sequence is irrelevant. In other words, if more than tw... Full Answer >
Filed Under:
PEOPLE SEARCH FOR