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?

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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