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Different Types of Equations

4.18.6 Different Types of Equations

4.18.6 • Different Types of Equations

Cool Down

1.

A sequence is defined by f1=−3f1=−3, fn=fn−1+0.5fn=fn−1+0.5 for n≥2n≥2. Diego writes an equation for the nthnth term of the sequence as an=−3+(n−1)(0.5)an=−3+(n−1)(0.5). Is he correct? Explain how you know.

Compare your answer:

Yes. For example: Both definitions create a sequence that starts at –3 and increases by 0.5 each term.

2.

How would you describe the representation f1=−3f1=−3, fn=fn−1+0.5fn=fn−1+0.5 for n≥2n≥2 for Diego’s sequence?

Compare your answer:

It is the recursive definition of the sequence.

3.

How would you describe the representation of Diego’s sequence, an=−3+(n−1)(0.5)an=−3+(n−1)(0.5)?

Compare your answer:

This is the nthnth term of the sequence.