Math 1 · Unit 9 · Lesson 5 · part 2 of 5
Three moves: type, rule, answer
This lesson uses everything in the unit.
Three moves: type, rule, answer
This lesson uses everything in the unit. A real situation comes as a story, a table, or a picture pattern. Turn it into a sequence in three moves.
- 1Decide the type.Use the Unit 7, Lesson 5 check. Equal differences: arithmetic. Equal ratios: geometric. Neither: neither. Adding gives arithmetic, multiplying gives geometric.
- 2Write the rule.Arithmetic: start + d(n − 1). Geometric: start · rn − 1. Say what n counts.
- 3Answer the question.A far term: put in n. Which term reaches a value: set the rule equal to it, or build a table.
Always ask what n counts, and where the counting starts. The story decides. Pizza toppings start at 1 topping. An orchard in "year 0" starts at 0. If the first input is 1, the rule uses n − 1 steps. If the first input is 0, it uses n steps, and the start is the y-intercept itself.