Arithmetic & Geometric Sequences

Formulas & Rules

100

Which type of sequence uses adding and subtracting?

Arithmetic

200

Which type of sequence uses multiplying and dividing?

Geometric

300

Is this the Recurrence Relation for arithmetic or geometric sequences?

t₀=initial    t_n+1 = t_n + d

arithmetic

400

Is this the Recurrence Relation for arithmetic or geometric sequences?

t₀=initial,   t_n+1 = Rt_n

geometric

500

What does the R stand for in the formula for geometric sequences?

ratio

Arithmetic Adding

100

What is being added to each term to get the following term in the following arithmetic sequence?

11, 15, 19, 23, 27........

added 4

200

What is being added to each term to get the following term in the following arithmetic sequence?

3,6,9,12,15.....

added 3

300

What is being added to each term to get the following term in the following arithmetic sequence?

80,75,70,65,60......

added -5

400

What is being added to each term to get the following term in the following arithmetic sequence?

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

added 5

500

What is being added to each term to get the following term in the following arithmetic sequence?

5, -8, -21, -34, -47

added -13

Geometric Multiplying

100

What is each term being multiplied by to get the following term in the following geometric sequence?

1,2,4,8,16,32,64,128.....

multiplied by 2

200

What is each term being multiplied by to get the following term in the following geometric sequence?

10, 30, 90, 270, 810, 2430.........

multiplied by 3

300

What is each term being multiplied by to get the following term in the following geometric sequence?

4, -8, 16, -32, 64, -128.......

multiplied by -2

400

What is each term being multiplied by to get the following term in the following geometric sequence?

1000, 200, 40, 8........

Multiplied by 1/5

500

What is each term being multiplied by to get the following term in the following geometric sequence?

243, 81, 27, 9, 3, 1.....

Multiplied by 1/3

Arithmetic

100

What would the next term in the arithmetic sequence be?

15, 30, 45, 60, ____

75

200

What would the next term in the arithmetic sequence be?

92, 81, 70, 59, _____

48

300

Write the general rule for the following arithmetic sequence

-6, -1, 4, 9

t_n=-6+5n

400

What would the t₅ be?

-6, -1, 4, 9 ...

19

500

What would t₈₇ be?

-9, -2, 5, 12...

600

Geometric: missing term

100

What would the next term in the geometric sequence be?

3, 18, 108, ______

648

200

What would the next term in the geometric sequence be?

600, 300, 150, ____

75

300

What would the next term in the geometric sequence be?

4, 16, 64, 256, ______

1024

400

What would the next term in the geometric sequence be?

88, 440, 2200, ________

11,000

500

What would the next term in the geometric sequence be?

248 832,   20 736,   1728,  _____

144