Students will learn how to find the formula for a geometric sequence given two of its terms. Using the two terms, we can setup a system of two equations in two unknowns. Solving gives us the common ratio. Then plugging in the common ratio, and one of the known terms, we can find the value of the first term.
Next, give your students these challenges:
- 2019 Math Kangaroo Levels 7-8 Problem #25 Solution #1 by STEM4all
- 2020 AMC 8, Problem 6
- 2006 AMC 8, Problem 16
- 2014 AMC 8, Problem 1
- Paper Eight by Pierce School: Problem / Solution
Find the length of the diagonal line:
Here's the solution: The diagonal line is the hypotenuse of a right triangle, with legs of length \(3\) and \(2.\) Thus, the length of the diagonal is \(\sqrt{3^2 + 2^2} = \sqrt{13}\) (source.)
Conclude by leading this investigation:
My Pet Zebra
by MathPickle