Question

Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common difference

Answer 1

Problem 1

Answer: Arithmetic, common difference = -4

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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

Answer: Arithmetic, common difference = 5

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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

• -6+5 = -1
• -1+5 = 4
• 4+5 = 9

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

Answer: Not arithmetic

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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.