Geometric Sequences

Geometric Sequences

Geometric Sequences Review

Answer the questions and review the concepts as you go!

Geometric Sequence

A number sequence formed by multiplying a term in a sequence by a fixed number to find the next term.

Explicit Formula for a Geometric Sequence

a_n = a₁ (r)^n-1

Multiple Choice

What does r represent in the explicit formula for a geometric sequence?

• Radical

• Common Ratio

• Common Difference

Multiple Choice

Find the common ratio for the geometric sequence:

 $10,\ 20,\ 40,\ 80$  

• 10

• 1/2

• 2

• 4

Multiple Choice

Find the common ratio of the following geometric sequence

 $-250,\ -50,\ -10,\ 2$  

• r = 5

• r = -5

• r = 1/5

• r = -1/5

Multiple Choice

Is the following sequence geometric?

• Yes

• No

Multiple Choice

Is the following sequence geometric?

 $2,\ 4,\ 12,\ 48$  

• Yes

• No

Multiple Choice

 $3,\ 24,\ 192,\ 1536$  

Write the explicit formula for the following geometric sequence

•  $a_n=8\cdot3^{n-1}$  

•  $a_n=3\cdot8^{n-1}$  

•  $a_n=3+8\left(n-1\right)$  

Multiple Choice

Which formula is the recursive equation for a geometric sequence?

• $a_1=$
  

  $a_n=r\cdot a_{n-1}$
  

• $a_n=a_1+d\left(n-1\right)$

• $a_n=a_1\cdot r^{n-1}$

• $a_1=$
  $a_n=d+a_{n-1}$
  

Multiple Choice

Write the recursive formula for the following sequence

 $16,\ 8,\ 4,\ 2$  

•  $a_1=16$ 
  

   $a_n=\frac{1}{2}\cdot a_{n-1}$ 
  

•  $a_1=16$  
  

  
   $a_n=2\cdot a_{n-1}$  
  

•  $a_1=16$  
   $a_n=a_{n-1}-8$  
  

•  $a_1=16$  
  

  
   $a_n=a_{n-1}+0.5$  
  

Multiple Choice

Given the recursive formula, write the explicit formula for the geometric sequence.

 $a_1=6$  
 $a_n=5\cdot a_{n-1}$  

•  $a_n=5\cdot6^{n-1}$  

•  $a_n=6\cdot5^{n-1}$  

•  $a_n=6+5\left(n-1\right)$  

•  $a_n=5+6\left(n-1\right)$  

Thanks for playing!

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