Recognizing Arithmetic Sequences and Finding Common Difference

What do you call a set of numbers written in a special order by the application of a definite rule?

• Pattern

• Sequence

• Function

• Terms

Which of the following is not an arithmetic sequence?

• 1/2, 1, 3/2, 2

• 11, 14, 17, 20

• 2, 4, 8, 16

• 5, 2, -1, -4

Identify the next three terms of the sequence below:

• -17, -21, -25

• 17, 21, 25

• 18, 22, 26

• -18, -22, -26

What is the common difference of the given sequence?

5, 9, 13, ...

• 9

• 5

• 4

• not arithmetic

Answer explanation

To find the common difference, subtract the first term from the second: 9 - 5 = 4. This difference is consistent between the terms, confirming the sequence is arithmetic with a common difference of 4.

What is the common difference of the given sequence?

15, 9, 3, ...

• 6

• not arithmetic

• (-6)

• 15

Answer explanation

To find the common difference, subtract the second term from the first: 9 - 15 = -6. Then, check the next pair: 3 - 9 = -6. Since the difference is consistent, the sequence is arithmetic with a common difference of (-6).

What is the common difference of the given sequence?

12, 19, 26, ...

• -7

• 12

• 7

• not arithmetic

Answer explanation

To find the common difference, subtract the first term from the second: 19 - 12 = 7. Then, check the next pair: 26 - 19 = 7. Since the difference is consistent, the common difference is 7.

What is the common difference of the given sequence?

7, 9, 11, ...

• 4

• 7

• 2

• not arithmetic

Answer explanation

The sequence 7, 9, 11 is arithmetic because the difference between consecutive terms is constant. Subtracting 7 from 9 gives 2, and subtracting 9 from 11 also gives 2. Thus, the common difference is 2.

What is the common difference of the given sequence?

20, 29, 38, ...

• 38

• 20

• 9

• not arithmetic

Answer explanation

To find the common difference, subtract the first term from the second: 29 - 20 = 9. This is consistent for the next terms as well (38 - 29 = 9). Thus, the common difference is 9.

What is the common difference of the given sequence?

-25, -20, -15, -10,...

• not arithmetic

• -5

• 5

• -25

Answer explanation

The common difference in an arithmetic sequence is found by subtracting consecutive terms. Here, -20 - (-25) = 5, -15 - (-20) = 5, and -10 - (-15) = 5. Thus, the common difference is 5.

What is the common difference of the given arithmetic sequence?

• not arithmetic

• -13

• 12

• 25

Answer explanation

To find the common difference in the sequence 25, 12, -1, -14, subtract the first term from the second: 12 - 25 = -13. This difference is consistent between all consecutive terms, confirming the sequence is arithmetic with a common difference of -13.