Write the next three terms of the arithmetic sequence, then graph the sequence.$2,\ 8,\ 14,\ 20,\ ...$2, 8, 14, 20, ...The next three terms are , , and .
Question
Write the next three terms of the arithmetic sequence, then graph the sequence.2, 8, 14, 20, ...The next three terms are , , and .
Solution
To find the next three terms of an arithmetic sequence, we first need to determine the common difference. In this case, the difference between consecutive terms is 6 (8-2 = 6, 14-8 = 6, 20-14 = 6).
So, to find the next term, we add the common difference to the last term: 20 + 6 = 26.
To find the term after that, we add the common difference to the term we just found: 26 + 6 = 32.
Finally, to find the third term, we add the common difference to the second term we found: 32 + 6 = 38.
So, the next three terms of the sequence are 26, 32, and 38.
To graph the sequence, we can plot the terms on a number line or a coordinate plane. If we use a coordinate plane, we can let the x-axis represent the term number (n) and the y-axis represent the term value (a_n). The points would then be (1,2), (2,8), (3,14), (4,20), (5,26), (6,32), and (7,38).
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