Arithmetic and Geometric Sequences

Arithmetic or Geometric?

100

-4, 2, -1, 1/2

What is Geometric?

200

2 1/2 , 3, 3 1/2, 4, 4 1/2...

What is Arithmetic?

300

2, 4, 6, 8...

What is Arithmetic?

400

-2, -4, -8, -16...

What is Geometric?

500

The sequence -5, -10, -15, -20

What is what is arithmetic?

Common Difference

100

The Common Difference of -20, -23, -26, -29...

What is -3?

200

The Common Difference of -1.7, -2.0, -2.3, -2.6...

What is -0.3 ?

300

The Common Difference of 18, 22, 26, 30...

What is 4?

400

The Common Difference of 100, 131, 162, 193...

What is 31?

500

The Common Difference of 2.53, 2.56, 2.59, 2.62...

What is 0.03?

Common Ratio

100

The Common Ratio of the Sequence 2, 4, 8, 16, 32...

What is 2?

200

The Common Ratio of -1/2, 1, -2, 4...

What is -2?

300

The Common Ratio of the Sequence 3, 9, 27, 81...

What is 3?

400

The Common Ratio of the Sequence -3, -1, -1/3...

What is 1/3?

500

The Common Ratio of the Sequence -1000, 200, -40, 8...

What is - 1/5 ?

Writing Equations (Geometric)

100

Write an equation for the nth term of the geometric sequences.

3, 15, 75, 375, 1875, ... 

a_n = 3(5)^n-1

200

Write an equation for the nth term of the geometric sequences. 

324, 108, 36, 12, 4, ...

a_n = 324(1/3)^n-1

300

Write an equation for the nth term of the geometric sequences. 

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

a_n = 1(-2)^n-1

400

Write an equation for the nth term of the geometric sequences. Then find a₈

3, 6, 12, 24, ...

a₈ = 3(2)^8-1

a₈ = 3(2)

a₈ = 3(128) 

a₈ = 384

500

Write an equation for the nth term of the geometric sequences. Then find a₁₀

128, 64, 32, 16, 8, ...

a = 128(1/2)^10-1

a = 128(1/2)⁹

a = 128(1/512)

a = 128/512 or 0.25

Writing Equations (Arithmetic)

100

Write an equation for the nth term of the arithmetic sequences. 

1, 4, 7, 10, 13, ...

a_n = 1 + 3(n-1)

a_n= 1 + 3n - 3

a_n = 3n -2 

200

Write an equation for the nth term of the arithmetic sequences. 

3, 8, 13, 18, 23, ...

a_n = 3 + 5(n-1)

a_n = 3 + 5n - 5

a_n = 5n -2 

300

Write an equation for the nth term of the arithmetic sequences. 

-8, -2, 4, 10, 16, ...

a_n = -8 + 6(n-1)

a_n = -8 + 6n - 6

a_n = 6n - 14

400

Write an equation for the nth term of the arithmetic sequences. Then find a₇.

-6, 1, 8, 15, 22, ...

a₇ = -6 + 7(7 - 1) 

a₇ = -6 + 7(6)

a₇ = -6 + 42 

a₇ = 36

500

Write an equation for the nth term of the arithmetic sequences. Find a₁₀

11, 4, -3, -10, -17, -24, ...

a₁₀ = 11 + -7(10-1)

a₁₀ = 11 + -7(9)

a₁₀ = 11 - 63

a₁₀ = -52