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Chapter 8: Problem 76

What is a geometric sequence? Give an example with your explanation.

Short Answer

Expert verified
A geometric sequence is a sequence where each term is the result of the previous term multiplied by a fixed, non-zero number called the common ratio. For example, in the sequence 3, 6, 12, 24, ..., each term is twice the previous term.

Step by step solution

01

- Definition

A geometric sequence is a sequence of numbers where each term after the first one is the result of the previous term multiplied by a fixed, non-zero number called the common ratio. This can be expressed as: \[a, ar, ar^2, ar^3, ...\] where 'a' is the first term and 'r' is the common ratio.
02

- Example of a Geometric Sequence

For instance, consider the sequence: \[3,6,12,24,...\]. This is a geometric sequence because each term is twice the predecessor. Here, 'a' is 3 (the first term), and 'r' is 2 (the common ratio, because each term is twice the previous one).

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Most popular questions from this chapter

Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. $$ \begin{array}{l}f_{1}(x)=(x+2)^{3} \\\f_{2}(x)=x^{3} \\\f_{3}(x)=x^{3}+6 x^{2} \\\f_{4}(x)=x^{3}+6 x^{2}+12 x \\\f_{5}(x)=x^{3}+6 x^{2}+12 x+8\end{array} $$ Use a \([-10,10,1]\) by \([-30,30,10]\) viewing rectangle.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (2 a+b)^{6} $$

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(y^{3}-1\right)^{20} $$

What is an annuity?

Find the term indicated in each expansion. \((x+2 y)^{10} ;\) the term containing \(y^{6}\)
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