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Answer the questions about the sequence below.

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Is the sequence arithmetic or geometric?
Does it have a common difference or common ratio?
What is the common difference or common ratio?
What are the next three terms?


−8, −3, 2, 7, 12, . . .

1 answer

To determine whether the sequence is arithmetic or geometric, we need to examine the differences between consecutive terms.

The given sequence is: −8, −3, 2, 7, 12, . . .

Step 1: Find the Differences

Now, let's find the differences between consecutive terms:

  • The difference between −3 and −8 is: \(-3 - (-8) = -3 + 8 = 5\)

  • The difference between 2 and −3 is: \(2 - (-3) = 2 + 3 = 5\)

  • The difference between 7 and 2 is: \(7 - 2 = 5\)

  • The difference between 12 and 7 is: \(12 - 7 = 5\)

Step 2: Determine Type of Sequence

Since the difference between each pair of consecutive terms is constant and equal to \(5\), the sequence is arithmetic.

Conclusion

  • Is the sequence arithmetic or geometric?

    • It is arithmetic.

  • Does it have a common difference or common ratio?

    • It has a common difference.

  • What is the common difference or common ratio?

    • The common difference is \(5\).

Step 3: Find the Next Three Terms

To find the next three terms, we simply add the common difference \(5\) to the last term:

  • Next term after \(12\): \(12 + 5 = 17\)

  • Next term after \(17\): \(17 + 5 = 22\)

  • Next term after \(22\): \(22 + 5 = 27\)

Final Answer

The next three terms of the sequence are: 17, 22, 27.