Arithmetic and Geometric Sequences

Arithmetic

100

The formula for an arithmetic sequence

 f(_n)=d+(n)(r)

200

Find the 9th term:

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

_N9= (53)+(9)(-3)

_N9=26

300

What is the common difference in this sequence?

31, -69, -169, -269

d= -100

400

Find the 29th term:

11, 20, 29, 38...

A₃₀= (11)+(29)(9)

A₃₀= 272

500

Find the number of terms in the following sequence:

9, 5, 1...-251

n= 66

Geometric

100

The formula for a Geometric sequence

_f(n)=d(r)⁽ⁿ⁾

200

Find the 6th term:

2, 6, 18, 54...

_N(6)=(2)(3)⁽⁶⁾

_N6= 1,458

300

What is the common ratio in this sequence?

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

r= 2

400

Find the 8th term:

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

A₈= (-2)(-5)⁽⁸⁾

A₈= 781,250

500

Find the number of terms in the following sequence:

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

2, 4, 8, 16, 32,... 1024

n= 10

Variable Vocab

100

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

"n" stands for the term number/position

200

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

"d" stands for the first term 

300

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

"r" stands for common difference/common ratio

400

arithmetic sequence involves what type of math operation?

addition and subtraction

500

geometric sequence involves for what type of math operation?

multiplication

Identify the Sequence

100

Arithmetic, geometric, or neither? 

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

Arithmetic

d= -20

200

Arithmetic, geometric, or neither?

22, 44, 66, 88...

Arithmetic

d= 22

300

Arithmetic, geometric, or neither?

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

Geometric

r= -2

400

Arithmetic, geometric, or neither?

4, 8, 16, 32,...

Geometric

r= 2

500

Arithmetic, geometric, or neither?

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

Neither

Its Fibonacci's sequence B-)

Complete the Sequence

100

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

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

r= 2

n₅= -16

200

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

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

r= -4

_n5= -16

_n6= -20

300

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

-1, -0.5, -0.25, -0.125, __, __, __, __,...

r= 1/2

_n5= -0.0625

_n6= -0.03125

_n7= -0.015625

_n8= -0.0078125

400

Find the first and fifth terms

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

r= -5

_n1= -2

_n5= -1,250

500

Find the first and fourth terms 

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

d= 9

_n1= 11

_n4= 38