Write the next three terms of the arithmetic sequence, then graph the sequence.$13,\ 7,\ 1,\ -5,\ ...$13, 7, 1, −5, ...The next terms are , , and .
Question
Write the next three terms of the arithmetic sequence, then graph the sequence.
Given the sequence:
13, 7, 1, -5, ...
The next terms are
..., ..., and ....
Solution
The common difference in this arithmetic sequence is -6 (7-13 or 1-7 or -5-1).
To find the next three terms, we subtract 6 from the last given term (-5) successively:
-5 - 6 = -11 (next term) -11 - 6 = -17 (next term) -17 - 6 = -23 (next term)
So, the next three terms are -11, -17, and -23.
To graph the sequence, you would plot the terms on a graph with the term number on the x-axis and the term value on the y-axis. The points would be (1,13), (2,7), (3,1), (4,-5), (5,-11), (6,-17), and (7,-23). The graph would show a straight line descending from (1,13) to (7,-23).
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