Question

Brian is building a triangle sequence so that two triangles are added to the right each time as shown below how many matchsticks will he use for the nth figure and for the figure one before the nth?the nth figure will take ______ matchstick's to build. (Type an expression using n as the variable. simplify the answer)

Answer 1

Given:

The initial matchsticks used: 3

We noticed that they increased by 4 or the common difference is 4, so they are

3,7, 11

We use arithmetic sequence formula:

`\begin{gathered} a_n=a_1\text{ + }(n-1)\text{ d} \\ \text{where:} \\ a_1\text{ = first term} \\ d=\text{ }common\text{ difference} \end{gathered}`

We plug in what we know:

`\begin{gathered} a_{n\text{ }}=a_{1_{}}\text{ + (n-1) d} \\ \text{= 3 + (n-1) 4} \\ \text{Simplify} \\ \text{= 3+ 4n-4} \\ \text{=4n-1} \end{gathered}`

Therefore, the nth figure will take 4n-1 matchsticks to build.