Practice Infinite Geometric Series (4) - Geometric Sequences - IB 10 Mathematics

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6 sample questions

Question 1.
Find the sum of the infinite series: 4 + 2 + 1 + ...
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Identify the first term and the ratio, then apply the formula.
Question 2.
What is the common ratio in the series: 3, 1.5, 0.75, ... ?
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Divide one term by the previous one.
3Question 3.
What condition must the common ratio meet for an infinite geometric series to converge?
- r > 1
- |r| < 1
- |r| = 1
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Think about how the terms behave when we reach infinity.
4Question 4.
The sum of an infinite geometric series can be calculated with which formula?
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Remember the components: first term and common ratio.
Question 5.
You have an infinite geometric series with the first term 8 and a common ratio of 0.3. Find the convergence sum.
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Use the sum formula provided earlier.
Question 6.
If you deposit $2000 with an interest rate of 3% compounded annually and let it work for infinitely many years, what would be the total value?
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Remember to account for the terminating behavior of the series.

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