Sequences and series

Which statement is true about the series shown below?
-4 + -2 + -1 + ½ + -¼+ ...

• The series converges because ∣r∣ < 1
• The series diverges because ∣r∣ < 1
• The series converges because ∣r∣ > 1
• The series diverges because ∣r∣ > 1

Select the picture that represents the formula for the sum of an infinite geometric series.

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What best describes the following infinite geometric series:

1/3 - 1/9 + 1/27 - 1/81 + ...

• Diverges because r=-1/3

• Converges because r=-1/3

• Converges because r=-3

• Diverges because r=-3

 $1-\frac{1}{5}+\frac{1}{25}-\frac{1}{125}+...$  Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.

• Convergent, 5/4

• Convergent, 5/6

• Divergent

A pendulum that is released to swing freely travels 18 cm on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

The sum of an infinite Geometric series is given by:

• $S=\frac{r}{1-a}$

• $S_n=\frac{a\ \left(1-r^n\right)}{1-r}$

• $S_n=\frac{a}{1-r^n}$

• $S=\frac{a}{1-r}$

Find the sum of the the following series:
1 +  $\frac{1}{7}$   +  $\frac{1}{49}$   +  $\frac{1}{343}$  
Formula provided above.

•  $\frac{9}{8}$  
  

•  $\frac{7}{6}$  

•  $\frac{4}{3}$  

•  $\frac{6}{5}$  

• 1.1
• 1.111
• 0.222
• 1.9

Which of the following is DIVERGENT?

• $\frac{1}{2}+1+2+4+8+...$

• $100+25+6.25+...$

• $a_n=5\left(\frac{3}{4}\right)^{n-1}$
  

• $a_1=3,\ r=0.5$
  

• Converges to 0

• Converges to 1

• Converges to 3

• Diverges