Question

Erica is collecting cans for a school fundraiser. She collects 5 the first day, 10 the second day, and 15 the third day. if the pattern continues, how many cans will she collect on the tenth day? A) 50 cans B) 15 cans C) 100 cans D) 65 cans

Answer 1

A) 50 cans

1) We can write the sequence of collecting cans like this for Erica:

`(5,10,15,\ldots\text{.)}`

2) Note that this is an Arithmetic Sequence and this can be described by the following explicit formula since the common difference is 5, the first element is 5:

`a_n=5+(n-1)d`

3) So let's find out the tenth term of that sequence

`\begin{gathered} a_(10)=5+(10-1)5 \\ a_(10)=5+(9)5=50 \end{gathered}`

Hence, on the tenth day She will collect 50 cans