Math Sequences

Which of the following sequences is an arithmetic sequence?

• 1, 3, 6, 10

• 2, 5, 8, 11

• 3, 6, 9, 12

• Both B and C

Answer explanation

An arithmetic sequence has a constant difference between consecutive terms. In sequence B (2, 5, 8, 11), the difference is 3. In sequence C (3, 6, 9, 12), the difference is also 3. Thus, both B and C are arithmetic sequences.

Tags

CCSS.HSF.BF.A.2

The 2nd term of an arithmetic sequence is 8 and the 4th term is 14. What is the 3rd term?

• 6

• 10

• 12

• 11

Answer explanation

In an arithmetic sequence, the difference between terms is constant. The 2nd term is 8 and the 4th term is 14, so the common difference is 3. The 3rd term is 8 + 3 = 11.

Tags

CCSS.HSF.BF.A.2

If the first term of an arithmetic sequence is d(1)=3 and the d(n)=d(n-1)+3, what is the 3rd term of the sequence?

• 6

• 12

• 9

• 15

Answer explanation

The first term d(1) is 3. The common difference is 3. The second term d(2) = d(1) + 3 = 6. The third term d(3) = d(2) + 3 = 9. Thus, the 3rd term of the sequence is 9.

Tags

CCSS.HSF.BF.A.2

Identify the common difference in the following arithmetic sequence: 2, 5, 8, 11, 14.

• 2

• 5

• 4

• 3

Answer explanation

In the sequence 2, 5, 8, 11, 14, the common difference is found by subtracting the first term from the second: 5 - 2 = 3. This difference remains consistent throughout the sequence, confirming that the correct answer is 3.

Tags

CCSS.HSF.BF.A.2

True or False: An arithmetic sequence CANNOT contain negative numbers.

• True

• False

Answer explanation

False is correct because an arithmetic sequence can include any real numbers, including negative numbers. For example, the sequence -3, -1, 1, 3 is an arithmetic sequence with a common difference of 2.

Tags

CCSS.HSF.BF.A.2

The next two terms of the sequence 4,7,10,13 are ....

• 16 and 19

• 15 and 19

• 16 and 18

• 15 and 18

Tags

CCSS.HSF.BF.A.2

Identify the common difference. 
10, 20, 30, 40, ...

• 5

• 10

• 15

• 20

Tags

CCSS.HSF.BF.A.2

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

• Arithmetic

• Geometric

• Neither

Tags

CCSS.HSF.BF.A.2

What is the common ratio of the geometric sequence below?
5, 25, 125, 625...

• 25

• 20

• 5

• 4

Tags

CCSS.HSF.BF.A.2

• 20

• 7

• 15

• 9

Tags

CCSS.HSF.BF.A.2