Julian’s math teacher, Ms. Pepperdine, has asked all of her students to memorize all of the perfect squares up to 202. Julian hates memorizing, so he is trying to identify a pattern that will make it easier. Homework Help ✎
He lists the first five perfect squares: 1, 4, 9, 16, 25 and looks for a pattern. “Hey, I see one! I add 3, then 5, then 7, then 9.” What does Julian mean? How can he find the next perfect square using his pattern?
How can Julian prove that his pattern will work for all perfect squares?
What is the pattern among the numbers he is adding?
If 2n must always result in an even integer,
what type of number must 2n + 1 always equal?
What equation would show give the next consecutive odd number in the series?
Combine the equation 2n + 1 with your equation from the Help before.
Simplify to find the proof that fits for all perfect squares.