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Chapter 11: Problem 90

Explain how to find the general term of a geometric sequence.

Short Answer

Expert verified
The general term of a geometric sequence can be found using the formula \(a*r^{(n-1)}\) where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.

Step by step solution

01

Understanding a Geometric Sequence

A geometric sequence is a sequence of numbers where the ratio of any two adjacent terms is always the same. This ratio is known as the common ratio, denoted by 'r'.
02

Identifying the First Term and Common Ratio

Given a geometric sequence, you need to identify the first term 'a' which is the first number in the series, and the common ratio 'r', which is the constant multiplied to each term to get to the next term.
03

Finding the nth term

The nth term of a geometric sequence can be found using the formula \(a*r^{(n-1)}\), where 'n' is the term number, 'a' is the first term, and 'r' is the common ratio.

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Most popular questions from this chapter

Exercises \(116-118\) will help you prepare for the material covered in the next section. In Exercises \(116-117\) show that $$1+2+3+\cdots+n=\frac{n(n+1)}{2}$$ is true for the given value of \(n\) $$ \text { Simplify: } \frac{k(k+1)(2 k+1)}{6}+(k+1)^{2} $$

Explaining the Concepts Explain how to find or probabilities with mutually exclusive events. Give an example.

Graph \(f(x)=x^{2} .\) Then use the graph of \(f\) to obtain the graph of of \(g(x)=(x+2)^{2}-1\)

Explaining the Concepts Describe the difference between theoretical probability and empirical probability.

You are dealt one card from a standard 52-card deck. Find the probability of being dealt $$\text{a card greater than 3 and less than 7.}$$
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