Question

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?

Answer 1

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