Mini Challenge: Arithmetic Sequence

Find the 10^th term in the sequence that starts with 1 and has a common difference of 3.

• 28

• 30

• 25

• 24

Answer explanation

To find the 10th term, use the formula: a_n = a_1 + (n-1)d. Substituting a_1=1, n=10, and d=3, we get a_10 = 1 + (10-1)3 = 1 + 27 = 28. Therefore, the 10th term is 28.

Tags

CCSS.HSF.BF.A.2

What is the next term in the sequence 11, 25, 39, ...?

Tags

CCSS.HSF.BF.A.2

If the sequence 4, 8, 12, 16 continues, what will be the 7^th term?

• 24

• 32

• 28

• 36

Answer explanation

The sequence increases by 4 each time: 4, 8, 12, 16, 20, 24, 28. Therefore, the 7th term is 28.

Tags

CCSS.4.OA.C.5

In the sequence 9, 18, 27, 36 and so on, what is the common difference?

• 9

• 5

• 11

• 7

Answer explanation

The common difference in the sequence is 9, as each term increases by 9 (9, 18, 27, 36, ...). Therefore, the correct answer is 9.

Tags

CCSS.HSF.BF.A.2

The difference between two terms in an arithmetic sequence is called ___________________.

• Formula

• Common Difference

• Common Ratio

• Common Factor

Answer explanation

The difference between two terms in an arithmetic sequence is called Common Difference.

Tags

CCSS.HSF.BF.A.2

Which of the following is an example of an arithmetic sequence?

• 4, 8, 16, 32, 64

• 1, 2, 4, 7, 11

• 3, 6, 12, 24, 48

• 15, 13, 11, 9, 7

Answer explanation

The correct example of an arithmetic sequence is 15, 13, 11, 9, 7 where each term decreases by 2, showing a consistent pattern of subtraction.

Tags

CCSS.HSF.BF.A.2

Find the common difference: 29, 21, 13, 5, ...

• d = -10

• d = -9

• d = -8

• d = -7

Answer explanation

To find the common difference, subtract each term from the next term. 29 - 21 = 8, 21 - 13 = 8, 13 - 5 = 8. Therefore, the common difference is -8.

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

Answer explanation

The next two terms in the sequence are obtained by adding 3 to each previous term. Therefore, the next two terms after 13 are 16 and 19.

Tags

CCSS.HSF.BF.A.2

• 7, 49, 343, 2401, 16807

• 3, 7, 11, 15, 19

• 4, 7, 10, 13, 16

• 4, 12, 36, 144, 576

Answer explanation

The arithmetic sequence starts at 4 with a common difference of 3. Therefore, the first five terms are 4, 4+3=7, 7+3=10, 10+3=13, and 13+3=16. Hence, the correct answer is 4, 7, 10, 13, 16.

Tags

CCSS.HSF.BF.A.2

• -4, 34, 72, 110, 148

• 38, 42, 46, 50, 54

• 38, -152, 608, -2432, 9728

• 38, 34, 30, 26, 22

Answer explanation

To find the first five terms of an arithmetic sequence, we start with the given first term a1 = 38 and common difference d = -4. The terms are: 38, 38 - 4, 38 - 2*4, 38 - 3*4, 38 - 4*4 = 38, 34, 30, 26, 22. Therefore, the correct answer is 38, 34, 30, 26, 22.

Tags

CCSS.HSF.BF.A.2