How Do You Calculate the Sum of an Arithmetic Sequence?

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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.

  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.