Ginoni the goat is at the bottom of a series of 7 boulders, each higher than the last. She wants to reach the top, where there is a huge patch of grass that she’d like to graze. Being an athletic goat, she sometimes bounds up two boulders at a time; otherwise, she just jumps up one. Ginoni can use both one-boulder and two- boulder leaps within an ascent. Starting at the bottom, in how many ways could she reach the grass at the top?
Investigate what happens for different numbers of boulders and explain the pattern of how many different ways she can ascend.