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14 February, 02:22

The number of cans in the layers of a display in a supermarket form an arithmetic sequence. The bottom layer has 28 cans; the next layer has 25 cans and so on until there is one can at the top of the display. How many cans are in the entire display?

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  1. 14 February, 02:35
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    Answer: 145 cans

    Step-by-step explanation:

    arithmetic sequence

    aₙ = a₁ + (n-1). r

    aₙ → last term

    a₁ → 1st term

    n → quantity of terms

    r → common difference

    a₁ = 1 (one can at the top)

    aₙ₋₁ = 25

    aₙ = 28

    To find out How many cans are in the entire display, we need the SUM of the arithmetic sequence: S = (a₁+aₙ) n/2



    S = (1+28). n/2

    n = ?

    aₙ = a₁ + (n - 1). r

    r = 28 - 25 = 3

    28 = 1 + (n - 1).3

    27 = (n - 1).3

    27/3 = (n - 1)

    9 = n - 1

    n = 9 + 1 = 10

    S = (1+28). n/2

    S = (1+28).10/2 = 29.10/2 = 29.5 = 145
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