Question
The first three terms of an arithmetic sequence are as follows. \( -17,-10,-3 \) Find the next two terms of this sequence. \( -17,-10,-3, \square: \square \)
Ask by Parry Ward. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The next two terms are 4 and 11.
Solution
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For the sequence -17, -10, -3, you can find the common difference by subtracting the first term from the second:
Difference = (-10) - (-17) = 7
Now, add this common difference to the last known term (-3) to obtain the next term:
Next term = (-3) + 7 = 4
Repeat the process to find the following term:
Following term = 4 + 7 = 11
Thus, the sequence extended by the next two terms is:
-17, -10, -3, 4, 11
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Simplify this solution Beyond the Answer
To find the next two terms of the sequence, we first need to identify the common difference. The difference between the second term (-10) and the first term (-17) is \( -10 - (-17) = 7 \). Likewise, the difference between the third term (-3) and the second term (-10) is also \( -3 - (-10) = 7 \). Thus, the common difference is 7. To find the next terms, we add 7 to the last term: 1. \( -3 + 7 = 4 \) 2. \( 4 + 7 = 11 \) Therefore, the next two terms are: \( -17, -10, -3, 4, 11 \)
