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Chapter 11: Problem 89

What is the common ratio in a geometric sequence?

Short Answer

Expert verified
The common ratio in a geometric sequence is found by dividing any term by the previous term.

Step by step solution

01

Understanding Geometric sequence

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 number is called the 'common ratio'.
02

Finding the Common Ratio

In a geometric sequence, to find the common ratio, you divide any term by the previous term. The result is the common ratio. Mathematically, if the sequence is \(a, ar, ar^2, ar^3, ...etc.\) where 'a' is the first term and 'r' is the common ratio, then \(r = a_{n+1} / a_n \).

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Most popular questions from this chapter

Use the formula for the value of an annuity to solve Exercises 77鈥�84. Round answers to the nearest dollar. To offer scholarship funds to children of employees, a company invests \(\$ 15,000\) at the end of every three months in an annuity that pays \(9 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.

You are dealt one card from a 52-card deck. Find the probability that you are dealt a 5 or a black card.

How do you determine if an infinite geometric series has a sum? Explain how to find the sum of such an infinite geometric series.

A single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time.
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