Question
The first three terms of an arithmetic sequence are as follows. \[ -28,-23,-18 \] Find the next two terms of this sequence. \[ -28,-23,-18,[], \square \]
Ask by West Chang. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The next two terms are -13 and -8.
Solution
An arithmetic sequence has a constant difference between consecutive terms. To find the common difference, subtract the first term from the second:
-23 - (-28) = -23 + 28 = 5
This difference is confirmed by the second pair of terms:
-18 - (-23) = -18 + 23 = 5
Now, add the common difference of 5 to the last given term (-18) to get the fourth term:
-18 + 5 = -13
Then, add the difference again to obtain the fifth term:
-13 + 5 = -8
Thus, the next two terms of the sequence are -13 and -8.
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Simplify this solution Mind Expander
In an arithmetic sequence, each term is generated by adding a constant difference to the previous term. Here, the difference between consecutive terms is \( -23 - (-28) = 5 \) and \( -18 - (-23) = 5 \). So the common difference is 5. To find the next two terms, you simply add 5 to the last term: 1. Fourth term: \( -18 + 5 = -13 \) 2. Fifth term: \( -13 + 5 = -8 \) So, the next two terms are \( -13 \) and \( -8 \). The complete sequence is: \[ -28, -23, -18, -13, -8 \]
