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Cogito

Algebra 2 · Chapter 7 · Lesson 3

Practice Worksheet

Infinite Geometric Series

Adding forever and still landing on a number.

12 problems · about 21 minutes · A-SSE.B.4

NameDate

Figure — use these to answer the problems

Set the base below 1 and watch the terms shrink toward zero. That is what makes the total finite.
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y = 1 · 0.5^x + 0
a, first term1
r, common ratio0.5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. First term 10, ratio 0.5. What is the infinite sum?

    Answer

  2. When does an infinite geometric series converge?

    • When the size of the ratio is below 1.
    • Whenever the ratio is positive.

  3. First term 4, ratio 0.5. Infinite sum?

    Answer

  4. First term 9, ratio 0.5. Infinite sum?

    Answer

  5. First term 1, ratio 0.8. Infinite sum?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. First term 3, ratio 0.25. Infinite sum?

    Answer

  2. Ratio 2. Does the series converge? Enter 1 for yes or 0 for no.

    Answer

  3. 0.5 + 0.05 + 0.005 + ... What is the sum, as a decimal to three places?

    Answer

Stretch Yourself

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

4 problems

  1. Which ratios give a convergent infinite series?

    • r = 0.3
    • r = −0.5
    • r = 1
    • r = 1.5
    • Tick every box that applies.

  2. First term 20, ratio 0.5. Infinite sum?

    Answer

  3. The Total

    First term 6, ratio 0.5. What is the infinite sum?

    Answer

  4. The Bouncing Ball

    A ball is dropped from 10 m and each bounce reaches 0.5 of the previous height. What is the total of all the bounce heights after the drop, in metres?

    Answerm