Arithmetic and Geometric Sequences

Arithmetic

Geometric

Variable Vocab

Identify the Sequence

Complete the Sequence

100

The formula for an arithmetic sequence

A_n=A₁+(n-1)(d)

100

The formula for a Geometric sequence

A_n=A₁(r)^(n-1)

100

What does "n" stand for in both arithmetic and geometric sequence equations?

"n" stands for the term number

100

Arithmetic, geometric, or neither?

-10, -30, -50, -70...

Arithmetic

d= -20

100

Find the common difference or ratio to find the next term of the sequence:

-1, -2, -4, -8, __

r= 2

A₅= -16

200

Find the 10th term:

53, 50, 47, 44, 41...

A₁₀= (53)+(10-1)(-3)

A₁₀=26

200

Find the 7th term:

2, 6, 18, 54...

A₇=(2)(3)^(7-1)

A₇= 1,458

200

What does "A₁"stand for in both arithmetic and geometric sequence equations?

"A₁" stands for the first term

200

Arithmetic, geometric, or neither?

22, 44, 66, 88...

Arithmetic

d= 22

200

Find the common difference or ratio to find the next 2 terms in the sequence

0, -4, -8, -12,__, __,...

d= -4

A₅= -16

A₆= -20

300

What is the common difference in this sequence?

31, -69, -169, -269

d= -100

300

What is the common ratio in this sequence?

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

r= 2

300

What does "d" stand for in arithmetic sequence equations?

"d" stands for common difference

300

Arithmetic, geometric, or neither?

-0.5, 1, -2, 4,...

Geometric

r= -2

300

Find the common difference or ratio to find the next 4 terms of the sequence

-1, -1/2, -1/4, -1/8, __, __, __, __,...

r= 1/2

A₅= -1/16

A₆= -1/32

A₇= -1/64

A₈= -1/128

400

Find the 30th term:

11, 20, 29, 38...

A₃₀= (11)+(30-1)(9)

A₃₀= 272

400

Find the 9th term:

-2, 10, -50, 250...

A₉= (-2)(-5)^(9-1)

A₉= 781,250

400

What does "r" stand for in geometric sequence equations?

"r" stands for common ratio

400

Arithmetic, geometric, or neither?

4, 8, 16, 32,...

Geometric

r= 2

400

Find the first and fifth terms

__, 10, -50, 250, __,...

r= -5

A₁= -2

A₅= -1,250

500

Find the number of terms in the following sequence:

9, 5, 1...-251

n= 66

500

Find the number of terms in the following sequence:

-1/2, -1/4, -1/8, -1/16,... -1/1024

n= 10

500

What does "r" stand for in an arithmetic sequence equation?

Nothing- "r", or common ratio, is not a part of Arithmetic sequences 🙂

500

Arithmetic, geometric, or neither?

1, 1, 2, 3, 5,...

Neither

Its Fibonacci's sequence B-)

500

Find the first and fourth terms

__, 20, 29, __, 47,...

d= 9

A₁= 11

A₄= 38