Discrete Mathematics

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Mathematical sequences can be used to model real life applications. Suppose you want to construct a movie theater in your town. The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and you need 50 rows of seats.

(a) Write the sequence for the number of seats for the first 5 rows

(b) How many seats will be in the last row?

(c) What will be the total number of seats in the theater?

  • Discrete Mathematics -

    a.
    C(n)=16+4n
    C(1)=16+4(1)=20
    C(2)=16+4(2)=24
    ...
    C(5)=16+4(5)=36

    b.
    C(50)=16+4(50)=?

    c.
    50
    ∑ C(i)
    i=1

    50
    ∑ 16+4i
    i=1

    16(50)+4sum(i)
    =800 + 4[ 50(1+50)/2 ]
    = 800+4(1275)
    = 5900

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