Problem preview

F-BF.1.a Warmup M2-014-A10-V03

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Write a recursive rule for a quadratic-looking sequence from its terms

Problem

For \(6,~11,~18,~27\), calculate the changing first differences and write them as \(2n+1\) for the transition to term \(n\). State \(a_{1}\), give the recurrence for \(n\ge~2\), and verify every listed term.

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aₙ = aₙ₋₁ + (2n + 1). Without an initial term a₁, the recurrence cannot generate the sequence.

a₁ = 6 and, for n ≥ 1, aₙ = aₙ₋₁ + (2n + 3). This gives a₂ = 13, not 11, and mixes indexing systems.

a₁ = 6 and, for n ≥ 2, aₙ = aₙ₋₁ + (2n + 3). This gives a₂ = 13, not 11.

a₁ = 6 and, for n ≥ 2, aₙ = aₙ₋₁ + (2n + 1). The differences are 5, 7, 9, so it generates 11, 18, and 27.

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Curriculum context

Course: Math II
Standard: F-BF.1.a
Category: Functions
Domain: Building Functions
Objective: Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type: Write a recursive rule for a quadratic-looking sequence from its terms