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  • Perplex

    Sequences & Series (Lesson 1/7)

    Arithmetic Sequences

    1 / 20

    The diagram to the right shows the first 3 rows of seating in an amphitheater. The rows are arranged in rings around a central stage.


    How many seats are there in the

    • first row?

    • second row?

    • third row?


    How many seats will there be in the ​9th​ row?

    Powered by Desmos

    In the example above, we see that the number of seats in each row is

    ​
    15,21,27…
    ​


    We call this a sequence, which simply means a list of numbers in a specific order. Most interesting sequences follow a pattern, for example:


    ​
    1+4​5+4​9+4​13+4​⋯
    ​


    ​
    3×3​9×3​27×3​81×3​⋯
    ​


    ​
    1,11+1​21+2​32+3​53+5​85+8​13⋯
    ​