Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A population of insects grows according to the recursive formula P_n = 2 * P_(n-1) - 50, where P_n is the population in week n, and P_0 is the initial population. If P_0 = 100, what is the population in week 2 (P_2)?
- A300
- B200
- C150
- D250
Show answer & explanationAnswer & explanation
Correct answer: D. 250
First, calculate P_1 using P_0: P_1 = 2 * P_0 - 50 = 2 * 100 - 50 = 200 - 50 = 150. Then, calculate P_2 using P_1: P_2 = 2 * P_1 - 50 = 2 * 150 - 50 = 300 - 50 = 250.
Why the other options are wrong
- A. This might be 2 * P_1, forgetting to subtract 50.
- B. This might be 2 * P_0 or an incorrect calculation for P_2.
- C. This is P_1, not P_2.
Recursive Sequence Evaluation
A recursive sequence defines each term based on one or more preceding terms. To evaluate a specific term, you must calculate all preceding terms starting from the initial term(s).
- Requires an initial term (or terms) to start the sequence.
- Each term is generated by applying a rule to the previous term(s).
- Calculation must be done step-by-step, in order.
Memory trick: Previous term is your NEXT step!