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Chapter 14: Problem 97

What is the common ratio in a geometric sequence?

Short Answer

Expert verified
The common ratio in a geometric sequence is the fixed, non-zero number that we multiply each term by to get the next term.

Step by step solution

01

Understanding geometric sequences

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number. This sequence has a specific pattern that we can use to identify it.
02

Identifying the common ratio

The fixed non-zero number that each term is being multiplied by to get to the next term is called the common ratio. For example, in the geometric sequence 3, 6, 12, 24, 48, we double (or multiply by 2) each term to get the next term. So, the common ratio is 2.

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Most popular questions from this chapter

Write the first four terms of each sequence whose general term is given. $$a_{n}=\frac{n^{2}}{n !}$$

Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To save money for a sabbatical to earn a master's degree, you deposit \(\$ 2000\) at the end of each year in an annuity that pays \(7.5 \%\) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.

Use the formula for the sum of the first n terms of a geometric sequence to solve. A job pays a salary of \(\$ 24,000\) the first year. During the next 19 years, the salary increases by \(5 \%\) each year. What is the total lifetime salary over the 20 -year period? Round to the nearest dollar.

A company offers a starting yearly salary of \(\$ 33,000\) with raises of \(\$ 2500\) per year. Find the total salary over a ten-year period.
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