Concept explainers
Whether an arithmetic sequence with common difference 0 and a geometric sequence with common ratio 1 have the same first n terms.
Answer to Problem 113E
The statement is true.
Explanation of Solution
Given information:
Arithmetic sequence and geometric sequence have same first term.
The
Every geometric sequence can be written in the following form.
Now, if common ratio becomes 1, then first n terms of the series will be
An arithmetic sequence of n terms, has the form
That is
Common difference can be defined by d.
nth term of the arithmetic sequence has the form
Where
Now, if common difference becomes 0, then first n terms of the series will be
Hence, first n terms of an arithmetic sequence with common difference 0 and a geometric sequence with common ratio 1 will be same.
Chapter 8 Solutions
Precalculus with Limits: A Graphing Approach
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