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