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Exercises Sequences, counting and probability

Example 2 from Algebra and Trigonometry, 13.3 Geometric Sequences

Writing the Terms of a Geometric Sequence

List the first four terms of the geometric sequence with $a_{1} = 5$ and $r = –2.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Multiply $a_{1}$ by $- 2$ to find $a_{2} .$ Repeat the process, using $a_{2}$ to find $a_{3},$ and so on.

$\begin{array}{l} a_{1} = 5 \\ a_{2} = - 2 a_{1} = - 10 \\ a_{3} = - 2 a_{2} = 20 \\ a_{4} = - 2 a_{3} = - 40 \end{array}$

The first four terms are ${5, –10, 20, –40} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

List the first five terms of the geometric sequence with $a_{1} = 18$ and $r = \frac{1}{3} .$

How did it go?

PreviousFinding Common Ratios Next Using Recursive Formulas for Geometric Sequences

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 13.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.