Concept explainers
To write next three terms of the geometric sequence:
And also plot the graph of the sequence.
Answer to Problem 19E
The next three terms of given geometric series are: 1280, 5120, and 20480.
Explanation of Solution
Given:
The given geometric sequence is:
Concept Used:
- In a geometric sequence, the ration between each pair of consecutive terms is the same, this ratio is called the common ratio.
- Each term of a geometric series is found by multiplying the previous term by the common ratio.
Calculation:
To write next three terms of the geometric sequence:
First find the common ratio of the sequence by dividing second term by first, as
Thus, common ration of the given geometric sequence is 4, that is, each term of the given geometric series can be found by multiplying the previous term by the common ratio 4.
Thus, next term of 320 will be:
Similarly, next term of 1280 is:
And, next term of 5120 is:
Thus, next three terms of given geometric series are: 1280, 5120, and 20480.
Now, to plot the graph of given sequence, first make a table of representing terms, say
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
5 | 20 | 80 | 320 | 1280 | 5120 | 20480 |
Now, using this table plot the graph of the given sequence by plotting the coordinates in above table:
Thus, graph of the sequence is represented by blue and red dots, as
Chapter 6 Solutions
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