Concept explainers
a.
To graph: The first five terms for the sequence
a.
Explanation of Solution
Given information:
The sequence
Graph:
Consider the sequence
For first five terms substitute values of n in the above expression.
For first term substitute n as 1.
For second term substitute n as 2.
For third term substitute n as 3.
For fourth term substitute n as 4.
For fifth term substitute n as 5.
Denote the x-coordinate as n and y-coordinate as
Interpretation:
The graph obtained by plotting the points for the first five terms of the sequence
b.
To describe: The graph of first five terms for the sequence
b.
Answer to Problem 2CFU
The graph is a straight line and points are plotted at equal distances from one other.
Explanation of Solution
Given information:
The sequence
Consider the sequence
For first five terms substitute values of n in the above expression.
For first term substitute n as 1.
For second term substitute n as 2.
For third term substitute n as 3.
For fourth term substitute n as 4.
For fifth term substitute n as 5.
Denote the x-coordinate as n and y-coordinate as
The graph obtained by plotting the points for the first five terms of the sequence
c.
To calculate: The common differenceof the sequence
c.
Answer to Problem 2CFU
The common differenceis
Explanation of Solution
Given information:
The sequence
Calculation:
Consider the sequence
For first five terms substitute values of n in the above expression.
For first term substitute n as 1.
For second term substitute n as 2.
For third term substitute n as 3.
For fourth term substitute n as 4.
For fifth term substitute n as 5.
The sequence is
Recall that a sequence with first term as
Compute the difference between the consecutive terms,
And
Therefore, common difference is
Each term is 1 less than the preceding term. The magnitude of difference between two terms is 1.
Therefore, it is an arithmetic sequence which is decreasing.
Chapter 12 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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