Arithmetic vs Geometric Sequences, Polynomial Operations

Arithmetic vs. Geometric Sequences, Polynomial Operations

Arithmetic and Geometric Sequences

Geometric - Exponential growth/decay (pattern is multiplying or dividing)

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Arithmetic - Linear growth/decay (pattern is adding or subtracting)​

4, 7, 10, 13, ...

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This is arithmetic because it is adding 3 each time​

2, 10, 50, 250, ...

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This is geometric because it is multiplying by 5 each time.​

​Characteristics

Multiple Choice

Arithmetic, geometric, or neither?

4, 9, 14, 19, ...

• Arithmetic

• Geometric

• Neither

Multiple Choice

Arithmetic, geometric, or neither?

1, 3, 7, 13, ...

• Arithmetic

• Geometric

• Neither

Multiple Choice

Arithmetic, geometric, or neither?

100, 50, 25, 12.5, ...

• Arithmetic

• Geometric

• Neither

EXPLICIT FORMULAS

Arithmetic sequence

Geometric sequence

​-a_1 is 1st term

-a_n is nth term

-n is the number of term you're finding​

​

​r is the common ratio

​d is the common difference

100, 20, 4, 4/5, ...

​Writing the explicit formula

0.25, 0.75, 1.25, 1.75 ....

Multiple Choice

What is the common ratio of the geometric sequence below?
5, 25, 125, 625...

• 25
• 20
• 5
• 4

Multiple Choice

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

• 1024, 2048, 4096

• 32, 8, 2

• 64, 32, 16

• 92, 66, 38

Multiple Choice

Find the common ratio: 64, -16, 4, -1, ...

• r = -8
• r = -1/4
• r = -4
• r = 4

Multiple Choice

Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)

• a_n = 4n + 29
• a_n = -4n + 25
• a_n = -4n + 29
• a_n = 4n + 25

Multiple Choice

Find the 10th term.

• 16
• 12
• 21
• 30

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Multiple Choice

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4
• 3
• 2
• 6

Multiple Choice

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

• $$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

• $$a_n=8\cdot3^{\left(n-1\right)}$$

• $$a_n=216-144\left(n-1\right)$$

• $$a_n=216\cdot3^{\left(n-1\right)}$$

Multiple Choice

Which of the following is an example of an arithmetic sequence?

• 4, 8, 16, 32, 64

• 1, 2, 4, 7, 11

• 15, 13, 11, 9, 7

• 3, 6, 12, 24, 48

Multiple Choice

Use the explicit formula to find the first four terms of the sequence. $$a_n=3+5\left(n-1\right)$$  

• 3, 15, 75, 375

• 3, 8, 13, 18

• 5, 8, 11, 14

• 5, 15, 45, 135

Multiple Choice

The difference between two terms in an arithmetic sequence is called ___________________.

• Formula

• Common Ratio

• Common Difference

• Common Factor

Multiple Choice

In the sequence 9, 18, 27, 36 and so on, what is the common difference?

• 5

• 7

• 9

• 11

Multiple Choice

What 3 terms come next in the sequence? 
144, 72, 36

• 36, 18, 9
• 18, 16, 9
• 18, 9, 4.5
• 4.5, 9, 16

Multiple Choice

Write the explicit formula for the sequence.

10, -2, -14, -26, ...

• $$a_n=10\cdot\left(-\frac{1}{5}\right)^{\left(n-1\right)}$$

• $$a_n=-2\cdot7^{\left(n-1\right)}$$

• $$a_n=10-8\left(n-1\right)$$

• $$a_n=10-12\left(n-1\right)$$

Multiple Choice

Find the explicit formula:
-23, -16, -9, -2, ...

• a_n = -23 + 7(n -1)
• a_n = -23 - 7(n -1)
• a_n = 7 - 23(n -1)
• a_n = 7 + 23(n -1)

Multiple Choice

Is the sequence arithmetic: -3, 3, -3, 3, ...

• Yes
• No

Multiple Choice

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

• 18
• 17
• 15
• 14

Multiple Choice

What is the common difference?

• −16
• 84
• 16
• 0

Polynomial operations Review

Add, subtract, and multiply

Multiple Choice

Find the difference.

(3- 2x + 2x²) - (3x²+4x-5)

• x² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Multiple Choice

Find the sum.

(2x² + 5x - 7) + (- 4x² + 6x+3)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x²+ 5x -7

• -2x² + 11x -4

Multiple Choice

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1
• -2x² - 11x -4
• 2x² + 5x -7
• -2x² + 11x -4

Multiple Choice

Find the sum.

(5x² -3x + 4) + ( -3x² +6x- 3)

• 3x² + 2x + 1

• 2x² + 3x +1

• 2x² + 5x - 7

• 3x² + 4x⁵ -7x

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Multiple Choice

What is the perimeter of the triangle shown?

• 9r²+r-5

• 9r⁴+r²-4

• 9r²-r+4

• 9r²+r-4

Two ways to multiply:

1. Distributive property method (FOIL)

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2. Box method

Multiple Choice

Simplify:
2x ( -2x -3)

• -4x - 3
• x² - 3
• -4x² - 6x
• -4x - 6

Multiple Choice

(x +2)(x + 3)

• x² + 5x + 6
• x² + x + 6
• x² + 5x + 5
• x² + 6x + 6

Multiple Choice

(2x - 1)(x + 2)

• 2x² + 3x - 2
• 2x² - 5x - 2
• 2x² + 3x + 2
• 2x² - 5x + 2

Multiple Choice

Multiply
(4x+3)(2x-1)

• 8x²-2x-3
• 8x-3
• 8x²+6x-3
• 8x²+2x-3

Multiple Choice

(x+10)(x-10)

• x²  - 100
• x² + 100
• x² + 20x - 100
• x² -20x + 100

Multiple Choice

Find the area of a square whose side length is a+b.

• a² - b²
• a² + b²
• a² + ab + b²
• a² + 2ab + b²

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21
• x³+5x+13x-21
• x³-3x²+7x-21
• x²+2x-3