f(n) = 5+3n where n is the number of steps after the first two. 7 steps is 20 faces.
Step-by-step explanation:
A sequence is a list of numbers that are related. The first number in the sequence is 5 since the first part of the stairs has 5 faces (5 squares, the dark don't count). Every time you add a "stair" you add 2 blocks - one underneath to support and one as the step. This adds 3 faces. So 5 becomes 8. Repeat and 8 becomes 11. You add 3 faces each time. So the sequence is
5, 8, 11, 14, 17,....
This is a constant pattern of adding 3 each time after the initial start. So we can write a rule. We start with 5 + 3(each stair step). So if the cube is 7 stairs high, that is 5 more repetitions of adding blocks after the start (remember the start has 2 steps already). So 5 + 3(5) = 20. 7 steps high will have 20 faces.
