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Week 3

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Tuesday

Tuesday - Learn & Practice: Arithmetic Sequences

I can represent arithmetic sequences using recursive and explicit formulas.

Short Lesson

Arithmetic Sequences Change by the Same Amount

An arithmetic sequence changes by the same amount from one term to the next. That constant change is called the common difference, d.

Recursive Formula

a1 = starting value

an = an-1+d, n >= 2

Explicit Formula

an = a1+(n-1)d

What to Notice

The first term and common difference show up in both forms.

Guided Examples

Write Recursive and Explicit Rules

Example 1

Consider the sequence 10, 14, 18, 22, ...

Find the first term, common difference, recursive rule, and explicit rule.

Step-by-step solution:

  1. a1=10 Identify the first term.
Example 2

Consider the sequence 20, 17, 14, 11, ...

This time, the common difference is negative.

Step-by-step solution:

  1. a1=20 Identify the first term.

Tuesday Practice

Use the First Term and Common Difference

Keep editing your answer as you learn from feedback.

Problem 1

Write the recursive formula for 8, 5, 2, -1, ...

Example format: a1=8, an=a(n-1)-3

Problem 2

Write the explicit formula for 3, 10, 17, 24, ...

Example format: an=3+(n-1)7

Problem 3

Find the 12th term of an=5+(n-1)3.

Problem 4

Identify the common difference in an=an-1+12.

Example format: 12 or d=12

Problem 5

Translate a1=4, an=an-1+6 into an explicit formula.

Example format: an=4+(n-1)6

Tuesday Reflection

Which formula helps you find the 100th term faster?

End of Tuesday

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