IA: 2.2 Geometric Sequences

IA: 2.2 Geometric Sequences

Multiple Choice

135, 45, 15, 5, ...

• yes; r = 1/3

• yes; r = 3

• yes; r = 5

• no

Multiple Choice

7, -14, 28, -56, ...

• yes; r = 2

• yes; r = 1/2

• yes; r = -2

• yes; r = -1/2

Multiple Choice

-9, -36, -144, -576, ...

• yes; r = -4

• yes; r = 1/4

• no

• yes; r = 4

Multiple Choice

3072, 768, 192, _____, _____, ______

• 768, 3072, 12288

• 48, 12, 3

• -48, 12, -3

• -48, -12, -3

Multiple Choice

-5, -25, -125, _____, _____, _____

• 625, 3125, 15625

• -625, 3125, -15625

• -625, -3125, -15625

• 625, -3125, 15625

Multiple Choice

-4, 20, -100, ...

What is the explicit formula?

•  $a_n=-4\left(5\right)^{\left(n-1\right)}$  

•  $a_n=4\left(-5\right)^{\left(n-1\right)}$  

•  $a_n=-4\left(-5\right)^{\left(n-1\right)}$  

•  $a_n=4\left(5\right)^{\left(n-1\right)}$  

Multiple Choice

1, 5, 25, ...

What is the 7th term of the sequence?

• 15,600

• 15,625

• 125

• 75

Multiple Choice

729, -243, 81, ...

What is the explicit formula?

• $a_n=81\left(\frac{1}{3}\right)^{\left(n-1\right)}$

• $a_n=729\left(-\frac{1}{3}\right)^{\left(n-1\right)}$

• $a_n=729\left(-3\right)^{\left(n-1\right)}$

• $a_n=729\left(3\right)^n$

Multiple Choice

8, 12, 18, ...

What is the 7th term in the sequence?

• 91.125

• 384

• 1

• 40.359

Multiple Choice

486, 162, 54, 27, ...

Write the recursive formula of the sequence.

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

  $a_1=486$
  

• $a_1=486$
  $a_n=a_{\left(n-1\right)}\cdot3$

Multiple Choice

2, 1/2, 1/8, 1/32, ...

Write the recursive formula of the sequence.

• 
  

  $a_1=2$
  $a_n=a_{\left(n-1\right)}\cdot4$
  

• $a_1=2$
  $a_n=a_{\left(n-1\right)}\cdot\frac{1}{4}$
  

Multiple Choice

 $a_1=-2$  
 $a_n=a_{\left(n-1\right)}\cdot-5$  
 What are the first five terms of the sequence?

• -2, -10, -50, -250, -1250

• 2, 10, 50, 250, 1250

• 2, -10, 50, -250, 1250

• -2, 10, -50, 250, -1250

Multiple Choice

 $a_1=9$  

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

What are the first five terms of the sequence?

• 9, 3, 1, 1/3, 1/9

• 1/9, 1/3, 1, 3, 9

• 9, 6, 3, 0, -3

• 9, 3, 1, 3, 9

Multiple Choice

 $g\left(n\right)=-70\cdot\left(\frac{1}{5}\right)^{\left(n-1\right)}$  
What is the recursive formula of the explicit formula above?

•  $f\left(1\right)=-70$  
   $f\left(n\right)=f\left(n-1\right)\cdot\frac{1}{5}$  
  

•  $f\left(1\right)=\frac{1}{5}$  
   $f\left(n\right)=f\left(n-1\right)\cdot-70$  
  

Multiple Choice

 $g\left(n\right)=80\cdot\left(\frac{3}{4}\right)^{\left(n-1\right)}$  
What is the recursive formula of the explicit formula given?

•  $g\left(1\right)=\frac{3}{4}$  
   $g\left(n\right)=g\left(n-1\right)\cdot80$  
  

•  $g\left(1\right)=80$  
   $g\left(n\right)=g\left(n-1\right)\cdot\frac{3}{4}$  
  

Multiple Choice

 $g\left(1\right)=3$  
 $g\left(n\right)=g\left(n-1\right)\cdot\left(-5\right)$  
What is the explicit formula of the recursive formula given?

•  $a_n=3\left(-5\right)^{\left(n-1\right)}$  

•  $a_n=-5\left(3\right)^{\left(n-1\right)}$  

Open Ended

Do you have any questions about this lesson?