Arithmetic and Geometric

Arithmetic and Geometric

Arithmetic Sequence

等差數列

• A1 - first term

• d - common ratio

• An = A1 + n ( d - 1 )

Geometric Sequence

等比數列

• r - common ratio

• An = A1 x r^(n-1)

• 
  

Multiple Choice

What is a₅ in the sequence defined as follows?
a_n = 5 ⋅ 2^(n-1) 

• a₅ = 160
• a₅ = 40
• a₅ = 10
• a₅ = 80

Multiple Choice

Which lists four consecutive terms of an arithmetic sequence?

• 1, 4, 9, 16, ...
• 3, 10, 17, 24, ...
• 1, 2, 4, 8, ...
• -5, 6, 10, 13, ...

Multiple Choice

Find the 10th term of this sequence:
{96, 48, 24, 12, ... }

• 3/16
• 1/2
• 6
• 3

Multiple Choice

What is the 38th term of this sequence?
{26, 22, 18, 14, ... }

• -4
• 10
• -122
• 174

Multiple Choice

Is this sequence Arithmetic, Geometric, or Neither?
{2, 9, 7, 14, 12, 19, ... }

• Arithmetic
• Geometric
• Neither

Multiple Choice

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

• Arithmetic
• Geometric
• Neither

Geometric Series

等比級數

• sum of all the terms of geometric sequence

• Sn = A1 ( 1 - r^n ) / 1 - r

Infinite Geometric Series

• Convergent - has certain sum

• Divergent - doesn't have certain sum

Convergent

• when the absolute value of common ratio is Less than 1

• Sn = A1 / 1 - r

Multiple Choice

 $\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$  Find the sum of the series if it exists.

• 4/5

• 5

• 6.5

• Does not exist

Multiple Choice

Find the sum of the infinite geometric series, if it exists. $\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+...$  

• 205

• 19.5

• 108.75

• Does Not Exist

Multiple Choice

Evaluate the infinite geometric series:

1 + 1/5 + 1/25 + ...

• 5/4

• 9/5

• 5/6

• 65/27

Multiple Choice

Which of the following is DIVERGENT?

• 2+4+8+16+...

• 25+5+1+0.2+...

• 100+50+25+5+...

• 3(.25)ⁿ = A_n

Multiple Choice

Which of the series below is CONVERGENT?

• a₁=4, 1.5a_n-1, n≥2
• a_n=-n²- 8n +106
• a_n = 5/10ⁿ
• a_n = 5n + 6

Multiple Choice

Find the sum of the infinite geometric series, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$  

• 8

• 8/5

• 10

• Does not exist

Multiple Select

Identify the colour of the leafs this flower

• Blue

• Red

• Yellow

• Green

Multiple Choice

What is the value of r the common ratio of this series 1+5+25+125,,?

• 1

• 4

• 5

• 156

Multiple Choice

What is the formula for the sum of the first n terms of a geometric sequence?

• $ar^n$
  

• $ar^{n-1}$
  

• $\frac{a\left(1-r^n\right)}{1-r}$

• None of these

Okay then, I will leave the computer to her.