Problem 67
Question
What is a sequence? Give an example with your description.
Step-by-Step Solution
Verified Answer
A sequence is an ordered list of elements where the arrangement of elements is crucial, usually determined by a rule. Examples include arithmetic sequence like 2, 4, 6, 8, ... and geometric sequence like 3, 6, 12, 24, ...
1Step 1: Define Sequence
A sequence is an ordered list of elements or objects. The elements in a sequence are typically distinguished by their positions. The order or arrangement of the elements in a sequence is crucial, and is usually determined by a rule that specifies the pattern or relationship between the elements.
2Step 2: Provide Examples
Two common examples of sequences include: \n1. Arithmetic Sequence: It is a sequence where each term is obtained by adding a constant difference to the previous term. For instance in the sequence 2, 4, 6, 8, ... , each term is obtained by adding 2 to the previous term. \n2. Geometric Sequence: It is a sequence where each term is obtained by multiplying the previous term by a constant factor. For instance in the sequence 3, 6, 12, 24, ... , each term is obtained by multiplying the previous term by 2.
Other exercises in this chapter
Problem 67
Research and present a group report on state lotteries. Include answers to some or all of the following questions: Which states do not have lotteries? Why not?
View solution Problem 67
A pendulum swings through an arc of 20 inches. On each successive swing, the length of the arc is \(90 \%\) of the previous length. After 10 swings, what is the
View solution Problem 67
Teachers' earnings \(n\) years after 1989 can be described by \(a_{n}=1472 n+29,060 .\) According to this model, what will teachers earn in \(2083 ?\) Describe
View solution Problem 68
Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 64 and 65
View solution