Arithmetic Sequences

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

• d = -10

• d = -9

• d = -8

• d = -7

Answer explanation

To find the common difference, subtract the second term from the first: 21 - 29 = -8. Checking further: 13 - 21 = -8 and 5 - 13 = -8 confirms the common difference is d = -8.

Tags

CCSS.HSF.BF.A.2

Find the common difference: 1, 201, 401, 601, ...

• d = 100

• d = 101

• d = 200

• d = 201

Answer explanation

To find the common difference, subtract the first term from the second: 201 - 1 = 200. Similarly, 401 - 201 = 200 and 601 - 401 = 200. Thus, the common difference is d = 200.

Tags

CCSS.HSF.BF.A.2

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

• 63, 72, 81

• 79, 88, 97

• 70, 79, 88

• 61, 70, 79

Answer explanation

The sequence increases by 9 each time: 25 + 9 = 34, 34 + 9 = 43, 43 + 9 = 52. Continuing this pattern, the next terms are 52 + 9 = 61, 61 + 9 = 70, and 70 + 9 = 79. Thus, the correct answer is 61, 70, 79.

Tags

CCSS.HSF.BF.A.2

What is the distance from one number to the next in a sequence of numbers that is represented by a (d) in an arithmetic sequence?

• Common denominator

• Common opposites

• Common domain

• Common difference

Answer explanation

In an arithmetic sequence, the distance between consecutive numbers is called the 'common difference' (d). This term specifically refers to the consistent amount added or subtracted to get from one term to the next.

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 sequence increases by 3 each time: 4+3=7, 7+3=10, 10+3=13. Continuing this pattern, 13+3=16 and 16+3=19. Thus, the next two terms are 16 and 19.

Tags

CCSS.HSF.BF.A.2

Identify the common difference.

10, 20, 30, 40, ...

• 5

• 10

• 15

• 20

Answer explanation

The sequence 10, 20, 30, 40 increases by 10 each time. The common difference is the amount added to each term to get the next term, which is 10.

Tags

CCSS.HSF.BF.A.2

• 11

• 5

• 23

• 14

Answer explanation

In the arithmetic sequence 11, 14, 17, 20, 23, 26, the 5th term is found by counting: 1st (11), 2nd (14), 3rd (17), 4th (20), and 5th (23). Thus, the 5th term is 23.

Tags

CCSS.HSF.BF.A.2

Given the recursive formula, find the 7th term of the arithmetic sequence.

• 3.4

• 11.8

• 2

• 10.4

Answer explanation

To find the 7th term of the arithmetic sequence, use the recursive formula. Starting from the first term, add the common difference repeatedly. The calculations lead to the 7th term being 10.4, which is the correct answer.

Tags

CCSS.HSF.BF.A.2

Given the recursive formula, find the 4th term of the sequence.

• 9

• -2

• -1

• 14

Answer explanation

To find the 4th term using the recursive formula, we calculate the previous terms step by step. Following the sequence, we arrive at the 4th term being 9, which matches the correct answer choice.

Tags

CCSS.HSF.BF.A.2

Determine the next 3 terms of the arithmetic sequence:

10, 13, 16, 19, ...

• 21, 24, 27

• 22, 25, 28

• 25, 28, 31

• 3, 6, 9

Answer explanation

The sequence increases by 3 each time. Starting from 19, the next terms are 19 + 3 = 22, 22 + 3 = 25, and 25 + 3 = 28. Thus, the next three terms are 22, 25, 28.

Tags

CCSS.HSF.BF.A.2