Sigma Notation: Arithmetic Series
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Introduction

    In this lesson, you will learn how to work with sigma notation. Here are the sections in this lesson.

    Before studying sigma notation, it is required that you first have a firm grasp of these mathematical topics.

    esson: Functions
    esson: Arithmetic Sequences and Series
    esson: Sigma Notation


    We will review sigma notation using another arithmetic series.

arithmetic series example

    To find the first term of the series, we need to plug in 2 for the n-value. To find the next term of the series, we plug in 3 for the n-value, and so on. We keep using higher n-values (integers only) until we get to our final value. Our final value is 12.

    This table will show us what those n-values are and their respective values evaluated within the expression.

table values input expression output

    Now, this means we know the terms of the series.

arithmetic series expansion

    We can calculate the sum of this series, again by using the formula. Be careful when determining the number of terms in this series. The number of terms is equal to one more than the difference between the final value and the initial value.

determining the number of terms in a series using initial final values

    So, n = 11, a1 = 14, and a11 = -6.

arithmetic series sum formula calculations

    So, our solution can be written...

arithmetic series sum

    To ensure that you understand this lesson, try this interactive quiz.

    uiz: Sigma Notation: Arithmetic Series


    Try this quiz, which is related to the sections above.

    uiz: Sigma Notation: Arithmetic Series


    Try these lessons, which are related to the sections above.

    esson: Functions
    esson: Arithmetic Sequences and Series
    esson: Sigma Notation
    esson: Sigma Notation: Geometric Series