Question

The students in a math class were exploring toothpick patterns. They made this table.

Then their teacher challenged them to use the variable n to write an expression for the number of toothpicks in Stage n.

Hadley thought, “The first stage has 3 toothpicks and then 2 toothpicks are added at every stage minus the first one.”
Brett thought, “The number of toothpicks is always 2 times the stage number plus 1.”
Laurence thought, “Two toothpicks are added at each stage, except the first stage, which has 3 toothpicks instead of 2.”

Each student wrote a correct expression. Based on the students’ thinking, which shows the expression that each one wrote?

A. Hadley: 3 + 2n Brett: 2n + 1 Laurence: 2n – 2 + 3
B. Hadley: 3 + 2(n – 1) Brett: 2n + 1 Laurence: 2n + 3
C. Hadley: 3 + 2(n – 1) Brett: 2n + 1 Laurence: 2n – 2 + 3
D. Hadley: 3 + 2(n – 1) Brett: 2n + 1 Laurence: 2n – n + 3

Answer 1

Answer:

C. Hadley: 3 + 2(n – 1) Brett: 2n + 1 Laurence: 2n – 2 + 3

Step-by-step explanation:

Answer 2

The correct expression that each wrote is Hadley: 3 + 2(n - 1), Brett: 2n + 1, Laurence: 2n -2 + 3.

What is an algebraic expression?

'Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.'

According to the given problem,

Hadley's expression = 3 + 2 (n-1)

This is because Hadley thought that first stage has 3 toothpicks. 2 toothpicks added at every stage minus the first one = 2( n - 1 )

The number of toothpicks, 2 times the stage plus 1 = 2n + 1

Two toothpicks added at each stage except first stage which has 3 toothpicks instead of 2 = 2n -2 + 3

Hence, we can conclude that option: C is the correct choice.

Learn more about algebraic expression here:

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