Exercise 21 Page 324

Calculate the difference and ratio between consecutive terms. Is either of these the same throughout the sequence?

Sequence Type: Geometric
Next three terms: 768, 3072, and 12 288
Graph

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We want to identify the given sequence as arithmetic, geometric, or neither. To do so we will calculate the difference and ratio between consecutive terms.

We can see above that the differences are not the same. However, the ratios are the same. Therefore, the sequence is a geometric sequence with a common ratio of 4. To find the next three terms, we multiply each consecutive term by 4.

To graph the sequence, we will let the horizontal axis represent the position of the term within the sequence — this is the domain — and the vertical axis will represent the value of the terms — the range.

Subchapter links

1 Exponential Functions p.322

2 Exponential Growth and Decay p.322

3 Comparing Linear and Exponential Functions p.323

4 Solving Exponential Equations p.323

5 Geometric Sequences p.324

6 Recursively Defined Sequences p.324

Exercise 21 Page 324

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