Answer the questions about the sequence below.

Question

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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, . . .




(3 points)

Answer 1

To determine whether the sequence \(-8, -3, 2, 7, 12, \ldots\) is arithmetic or geometric, we first look at the differences between the consecutive terms.

1. Finding the common difference:

   • From \(-8\) to \(-3\): \[ -3 - (-8) = -3 + 8 = 5 \]

   • From \(-3\) to \(2\): \[ 2 - (-3) = 2 + 3 = 5 \]

   • From \(2\) to \(7\): \[ 7 - 2 = 5 \]

   • From \(7\) to \(12\): \[ 12 - 7 = 5 \]

Since the difference between each pair of consecutive terms is the same (5), we can conclude that this is an arithmetic sequence.

2. Common difference:

   The common difference \(d\) is \(5\).

3. Finding the next three terms:

   • To find the next term after \(12\): \[ 12 + 5 = 17 \]

   • The term after \(17\): \[ 17 + 5 = 22 \]

   • The term after \(22\): \[ 22 + 5 = 27 \]

Thus, the next three terms in the sequence are \(17, 22, 27\).

Summary:

• The sequence is arithmetic.
• The common difference is \(5\).
• The next three terms are \(17, 22, 27\).