Arithmetic Sequences

7, 12, 17, 22, 27....

What is the explicit arithmetic equation?

• 5n + 2

• 4n + 3

• 5n + 7

• 5n

Tags

CCSS.HSF.BF.A.2

Is the sequence arithmetic?

17, 9, 1, -7, ...

• Yes

• No

Answer explanation

Yes, the sequence is arithmetic because the difference between consecutive terms is constant. The differences are: 9-17 = -8, 1-9 = -8, and -7-1 = -8. Since the common difference is the same, the sequence is arithmetic.

Tags

CCSS.HSF.BF.A.2

Find the next three terms in the arithmetic sequence:

-33, -24, -15, -6, ...

• -1, 7, 15

• -5, 2, 9

• 3, 12, 21

• -65, -73, -81

Answer explanation

The common difference in the sequence is 9 (-24 - (-33) = 9). Continuing this pattern, the next three terms are -6 + 9 = 3, 3 + 9 = 12, and 12 + 9 = 21. Thus, the next three terms are 3, 12, 21.

Tags

CCSS.HSF.BF.A.2

3, 12, 21, 30...

Write the arithmetic sequence equation.

Answer explanation

The sequence increases by 9 each time: 3, 12 (3+9), 21 (12+9), 30 (21+9). The nth term can be expressed as a_n = 3 + 9(n-1) = 9n - 6, confirming the correct choice is a_n=9n-6.

Tags

CCSS.HSF.BF.A.2

3, 12, 21, 30...

Find the 20th term

Answer explanation

The sequence increases by 9, 9, 9... Thus, it is an arithmetic sequence with a first term of 3 and a common difference of 9. The 20th term is calculated as 3 + (20-1) * 9 = 174.

Tags

CCSS.HSF.BF.A.2

3, 12, 21, 30...

Find the arithmetic explicit equation and determine

what term number is "120"?

• 9n - 6 = 120

  14th 

• 9n - 6 = 120

  15th 

• 9n - 6 = 120

  16th 

• 9n - 6 = 120

  17th 

Answer explanation

The sequence increases by 9, 9, 9... The nth term is given by 3 + 9(n-1). Setting this equal to 120, we solve for n: 3 + 9(n-1) = 120 leads to n = 14. Thus, '120' is the 14th term.

Tags

CCSS.HSF.BF.A.2

Find the sequence rule for the sequence

26, 19, 12, ...

Answer explanation

The sequence decreases by 7 each time: 26 to 19 (7), 19 to 12 (7). The general term can be expressed as a_n = -7n + 33, where n starts from 1. Thus, the correct choice is a_n = -7n + 33.

Tags

CCSS.HSF.BF.A.2

Find the 14th term

26, 19, 12, ...

Answer explanation

The sequence decreases by 7 each time: 26, 19, 12, ... The nth term can be found using the formula: a_n = 26 - 7(n-1). For n=14, a_14 = 26 - 7(13) = -65. Thus, the 14th term is -65.

Tags

CCSS.HSF.BF.A.2

Find the rule and determine what term in the sequence is -100

26, 19, 12, ...

Answer explanation

The sequence decreases by 7 each time: 26, 19, 12, ... Continuing this pattern, the 19th term is -100. Thus, the correct answer is the 19th term.

Tags

CCSS.HSF.BF.A.2

In his piggy bank, Bingo dropped $1.00 on the first day, $2.50 on the second day and $4 on the third day and so on. How much did he drop in his piggy bank on the 19th day?

• $25

• $26.50

• $28

• $29.50

Answer explanation

Bingo's deposits increase by $1.50 each day: $1.00, $2.50, $4.00, etc. The formula for the nth day is: $1 + $1.50(n-1). For the 19th day: $1 + $1.50(18) = $1 + $27 = $28. Thus, he dropped $28 on the 19th day.

Tags

CCSS.HSF.BF.A.2