Problem 1
<h3>
Answer: Arithmetic, common difference = -4</h3>
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Explanation:
Pick any term of the sequence, and subtract off the previous term to find that,
- term2 - term1 = -12 - (-8) = -12 + 8 = -4
- term3 - term2 = -16 - (-12) = -16 + 12 = -4
- term4 - term3 = -20 - (-16) = -20 + 16 = -4
Each time we get the same result, so that means we have an arithmetic sequence with common difference -4
This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.
Eg: term2 = term1 - 4 = -8-4 = -12.
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Problem 2
<h3>
Answer: Arithmetic, common difference = 5</h3>
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Explanation:
Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one
Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.
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Problem 3
<h3>Answer: Not arithmetic</h3>
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Explanation:
Unlike the previous two problems, this sequence is not arithmetic.
We can see that
- term2 - term1 = 12 - 3 = 9
- term3 - term2 = 48 - 12 = 36
The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.
This sequence is instead geometric because
- term2/term1 = 12/3 = 4
- term3/term2 = 48/12 = 4
- term4/term3 = 192/48 = 4
Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.
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