Problem preview

F-IF.3 Warmup M1-021-A07-V02

Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.

Decide whether explicit and recursive rules define the same sequence

Problem

Compare explicit \(a_{n}=3\cdot~2^{n-1}\), \(n\ge~1\), with recursive \(a_{1}=3\), \(a_{n}=2a_{n-1}\).

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verdict = different; explicit starts 6; recursive starts 3

verdict = same; explicit adds 2; recursive multiplies by 2

verdict = different; terms match initially but rules use different notation

verdict = same sequence; explicit = start 3, multiply by 2, terms 3,6,12; recursive = start 3, multiply by 2, terms 3,6,12

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Curriculum context

Course: Math I
Standard: F-IF.3
Category: Functions
Domain: Interpreting Functions
Objective: Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.
Problem type: Decide whether explicit and recursive rules define the same sequence