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Cogito

Integrated Math 1 · Chapter 5 · Lesson 1

Practice Worksheet

Arithmetic Sequences

Adding the same amount each time.

12 problems · about 20 minutes · F-BF.A.2, F-LE.A.2

NameDate

Figure — use these to answer the problems

Set the slope to the common difference. Arithmetic sequence terms sit on a straight line.
-10-10-5-5551010
y = 4x − 1
Common difference4
Value before the first term-1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. a₁ = 5, d = 4. What is the 10th term?

    Answer

  2. Why does the formula use n − 1 rather than n?

    • Reaching the nth term takes one fewer step than n.
    • Because sequences start at zero.

  3. 2, 5, 8, 11. Common difference?

    Answer

  4. 20, 15, 10, 5. Common difference?

    Answer

  5. a₁ = 4, d = 3. What is the 10th term?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. a₁ = 100, d = −7. What is the 5th term?

    Answer

  2. To reach the 12th term, how many steps from the first?

    Answer

  3. a₁ = 6, d = 5. What is the 8th term?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each sequence by whether it is arithmetic.

    Write each item under the heading it belongs to: 4, 9, 14, 19 · 30, 24, 18, 12 · 2, 4, 8, 16 · 1, 4, 9, 16

    Arithmetic

    Not arithmetic

  2. a₁ = 2, d = 6. What is the 15th term?

    Answer

  3. The Difference

    5, 12, 19, 26. What is the common difference?

    Answer

  4. The Term

    a₁ = 3 and d = 4. What is the 20th term?

    Answer