Evaluating Terms Iteratively from a Recursive Rule
Grade 9 students in California Reveal Math Algebra 1 learn to generate sequence terms by applying a recursive formula step-by-step. This skill explains that recursive formulas define each term using the previous one, so terms must be computed in order — you cannot jump directly to the fifth term without first finding the second, third, and fourth. Students practice both arithmetic sequences (adding a constant, like a1=5 with rule an = a(n-1)+3 giving 5, 8, 11, 14) and geometric sequences (multiplying by a constant, like a1=2 with rule an = 4·a(n-1) giving 2, 8, 32, 128).
Key Concepts
To generate terms from a recursive formula, start with the given initial term $a 1$ and repeatedly apply the recurrence relation to find each successive term:.
$$a 1 \text{ (given)}, \quad a 2 = f(a 1), \quad a 3 = f(a 2), \quad a 4 = f(a 3), \quad \ldots$$.
Common Questions
What is a recursive formula and how does it work?
A recursive formula defines each term using the term immediately before it. You start with the given initial term a1 and apply the rule repeatedly: a2=f(a1), a3=f(a2), and so on. Terms must be computed in order.
How do you evaluate terms iteratively from a recursive rule?
Start with the initial term a1, substitute it into the recurrence relation to find a2, then use a2 to find a3, continuing step-by-step. This process is called iterative evaluation.
Can you skip steps when using a recursive formula?
No. Because each term depends on the previous one, you cannot jump directly to a5 without first computing a2, a3, and a4 in sequence.
What is an example of an arithmetic recursive sequence?
Given a1=5 and an = a(n-1)+3, the first four terms are 5, 8, 11, 14. Each term is found by adding 3 to the previous term.
What is an example of a geometric recursive sequence?
Given a1=2 and an = 4·a(n-1), the first four terms are 2, 8, 32, 128. Each term is found by multiplying the previous term by 4.
Which unit covers this skill in Algebra 1?
This skill is from Unit 8: Exponential Functions in California Reveal Math Algebra 1, Grade 9.