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Week 3

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Thursday

Thursday - Apply & Connect

I can connect arithmetic sequences to linear functions by identifying rates of change and intercepts.

Short Lesson

Sequences Can Connect to Linear Rules

Arithmetic sequences follow a constant rate of change and can be represented using a linear relationship with a discrete domain: n=1,2,3,...

Common Difference

The common difference d plays the same role as the slope m.

First Term

The first term a1 is the value when n=1.

0th Term

Extending backward to n=0 helps identify the related y-intercept.

Guided Examples

Extend the Pattern Backward

Example 1

Consider the sequence 12, 17, 22, ...

Write the related linear rule.

Step-by-step solution:

  1. d=5 The sequence increases by 5 each term.
Example 2

Suppose f(n)=2n+5.

What is the first term?

Step-by-step solution:

  1. n=1 The first term happens at n=1.

Thursday Practice

Connect Sequence Information to Linear Form

Use the common difference as the slope and extend backward when you need the related y-intercept.

Problem 1

A sequence is 12, 17, 22, .... Write it as a linear function f(n).

Problem 2

Is a sequence continuous or discrete?

Choose one

Problem 3

In f(n)=-2n+10, what is the common difference?

Example format: -2 or d=-2

Problem 4

Find a1 for f(n)=4n+3.

Problem 5

If a1=20 and d=-4, write the related equation in y=mx+b form.

Thursday Reflection

How does extending the pattern to the 0th term help you write the related linear equation?

End of Thursday

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