Question

Tony's Donut Shop sold a total of 150 donuts in the first six hours it was open for the day. Each hour they sold six more donuts than they sold the previous hour. Show how many total donuts Tony's sold during the first three hours.

Answer 1

Arithmetic Sequence

In an arithmetic sequence, each term can be found by adding a fixed number, called the common difference to the previous term.

Being a1 the first term, d the common difference, the sum of n terms is given by

`S_n=(2a_1+(n-1)\cdot d)/(2)\cdot n`

We know Tony's Donut Shop sold a total of Sn = 150 donuts in the first n=6 hours. We also know each hour they sold d=6 more donuts than the previous hour.

We have all the data to use the equation above and find a1:

`(2a_1+(6-1)\cdot6)/(2)\cdot6=150`

Calculating:

`\begin{gathered} (2a_1+30)\cdot3=150 \\ \text{Dividing by 3:} \\ 2a_1+30=50 \end{gathered}`

Solving for a1:

a1 = 10

This means the first hour 10 donuts were sold.

The second hour 10+6 = 16 donuts were sold

The third hour 16+6 = 22 donuts were sold, for a total of:

10+16+22=48

Tony's sold 48 donuts during the first 3 hours