Questions: Ryan is building a matchstick sequence as shown below. How many matchsticks will he use for the nth figure if the pattern of adding two new squares horizontally and two vertically continues? The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)

Ryan is building a matchstick sequence as shown below. How many matchsticks will he use for the nth figure if the pattern of adding two new squares horizontally and two vertically continues?

The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)

Transcript text: Points: 0 of 1 Ryan is building a matchstick sequence as shown below. How many matchsticks will he use for the nth figure if the pattern of adding two new squares horizontally and two vertically continues? Click the icon to view the matchstick square figures. The $n$th figure will take $\square$ matchsticks to build. (Type an expression using $n$ as the variable. Simplify your answer.) More Info Print Done

Solution

Solution Steps

Step 1: Identify the pattern

Observe the given matchstick figures and identify the pattern in the number of matchsticks used.

Step 2: Count matchsticks in initial figures

Count the number of matchsticks in the first few figures to establish a pattern:

Figure 1: 12 matchsticks
Figure 2: 20 matchsticks
Figure 3: 28 matchsticks

Step 3: Determine the relationship

Determine the relationship between the figure number (n) and the number of matchsticks. Notice that each new figure adds 8 matchsticks to the previous figure.

Step 4: Formulate the expression

Formulate an expression for the nth figure. The pattern starts with 12 matchsticks and adds 8 matchsticks for each subsequent figure: \[ \text{Number of matchsticks} = 12 + 8(n - 1) \]

Step 5: Simplify the expression

Simplify the expression: \[ \text{Number of matchsticks} = 12 + 8n - 8 \] \[ \text{Number of matchsticks} = 8n + 4 \]