6.7 Geometric Series
Chapter
Chapter 6
Section
6.7
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Solutions 44 Videos

Determine whether the series is geometric. Justify your answer.

  • 4+20+100+500+...
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0.15mins
Q1a

Determine whether the series is geometric. Justify your answer.

  • -150+15-1.5+0.15-...
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0.23mins
Q1b

Determine whether the series is geometric. Justify your answer.

  • 3-9+18-54+...
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0.13mins
Q1c

Determine whether the series is geometric. Justify your answer.

  • 256-64+16-4+...
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0.36mins
Q1d

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_8 for 2+6+18+...

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0.33mins
Q2a

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_{10} for 24-12+6-...

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1.21mins
Q2b

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_{15} for 0.3 +0.003+0.00003...

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1.14mins
Q2c

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_{12} for 1-\frac{1}{3}+\frac{1}{9}-...

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0.57mins
Q2d

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_9 for 2.1-4.2+8.4-...

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0.41mins
Q2e

For the geometric series, determine the values of a and r. Then, determine the indicated sum.

S_{40} for 8-8+8-...

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0.22mins
Q2f

Determine S_n for each geometric series.

a=6, r=2, n=9

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0.25mins
Q3a

Determine S_n for each geometric series.

f(1)=2, r=-2, n=12

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0.32mins
Q3b

Determine S_n for each geometric series.

f(1)=729, r=-3, n=15

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0.39mins
Q3c

Determine S_n for each geometric series.

f(1)=2700, r=10, n=8

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0.30mins
Q3d

Determine S_n for each geometric series.

a=\frac{1}{2}, r=4, n=8

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0.27mins
Q3e

Determine S_n for each geometric series.

a=243, r=\frac{1}{3}, n=10

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1.03mins
Q3f

Determine the sum of each geometric series.

27+9+3+...+\frac{1}{243}

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1.25mins
Q4a

Determine the sum of each geometric series.

75+3.5+1.75+...+0.10937

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1.25mins
Q4b

Determine the sum of each geometric series.

1200+120+12+...+0.0012

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1.56mins
Q4c

Determine the sum of each geometric series.

\displaystyle \frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\frac{8}{81}+...+ \frac{128}{6551}

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1.35mins
Q4d

Determine the sum of the geometric series.

5-15+45-...+3645

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1.39mins
Q5a

Determine the sum of the geometric series.

6-12+24-48+...-768

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0.56mins
Q5b

Determine the sum of the geometric series.

96 000-48 000+24 000-...+375

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2.01mins
Q5c

Determine the sum of the geometric series.

1-\frac{2}{3}+\frac{4}{9}-...+\frac{64}{729}

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1.36mins
Q5d

Determine the specified sum for the geometric series.

S_{10} for \sqrt{3}-3+3\sqrt{3}+...

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1.09mins
Q6a

Determine the specified sum for the geometric series.

S_{12} for \sqrt{2}x+2x+2\sqrt{2}x+...

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1.18mins
Q6b

Determine the specified sum for the geometric series.

S_{15} for 3+3x+3x^2...

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1.07mins
Q6c

Determine the sum of the geometric series.

10+5+\frac{5}{2}+...+\frac{5}{64}

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2.12mins
Q7a

Determine the sum of the geometric series.

1+x+x^2+x^3+...+x^k

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0.41mins
Q7c

The sum of 4+12+36+108+...+t_n is 4372. How many terms are in this series?

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1.33mins
Q8

The third term of a geometric series is 24 and the fourth term is 36. Determine the sum of the first 10 terms.

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1.56mins
Q9

In a lottery, the first ticket drawn wins a prize of $25. Each ticket drawn after that receives a prize that is twice the value of the preceding prize.

(a) Write a function to model the total amount of prize money given away.

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0.46mins
Q11a

In a lottery, the first ticket drawn wins a prize of $25. Each ticket drawn after that receives a prize that is twice the value of the preceding prize.

(b) Graph the function to determine how many prizes can be given out if the total amount of prize money is $2 million.

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0.45mins
Q11b

A bouncy ball bounces to \frac{2}{3} of its height when dropped on a hard surface. Suppose the ball is dropped from 20 m.

(a) What height will the ball bounce back up to after the sixth bounce?

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2.37mins
Q12a

A bouncy ball bounces to \frac{2}{3} of its height when dropped on a hard surface. Suppose the ball is dropped from 20 m.

(b) What is the total distance travelled by the ball after 10 bounces?

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1.46mins
Q12b

The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.

  • A hot-air balloon rises 40 m in the first minute. After that, the balloon rises 75\% as far as it did in the previous minute. How far does it rise in each of the next 3 min? Write these distances as a sequence.
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0.44mins
Q14a

The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.

  • Determine a function to represent the height of the balloon after $n$ minutes.Is this function continuous or discrete? Explain your reasoning and write the domain of the function.
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0.45mins
Q14b

The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.

Use the function \displaystyle f(b) = 160(1-0.75^n) to determine the height of the balloon after 10 min.

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0.15mins
Q14c

Three numbers, a, b, and c, form a geometric series so that a+b+c=35 and abc=1000. Determine the values of a, b, and c.

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2.47mins
Q15

For a geometric series \frac{S_4}{S_8}=\frac{1}{17}. Determine the first three terms of the series if the first term is 3.

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1.43mins
Q16

The sum of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. If the fourth term is 48, determine a, r, t_{10}, and S_{10}.

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3.56mins
Q17

Determine n if 3+3^2+3^3+..+3^n=9840.

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0.48mins
Q18

If 2b-2, 2b+2 and 5b+1 are the first three terms of a geometric sequence, determine the sum of the first five terms.

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3.18mins
Q19
Lecture on Geometric Series 8 Videos

1 Introduction to Geometric Series with an example

\displaystyle \begin{array}{lll} &S_n = \frac{a(r^n - 1)}{r -1}, \text{ if } &|r| >1 \\ &S_n = \frac{a(1- r^n )}{1 - r}, \text{ if } &|r| <1 \end{array}

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1.54mins
1 Introduction to Geometric Series with an example

2 Geometric Series without using the Formula

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2.07mins
2 Geometric Series without using the Formula

7 Infinite repeating decimals as Geometric Series

\displaystyle \begin{array}{lll} &S_{\infty} = \frac{a}{1 - r}, \text{ if } &|n| <1 \end{array}

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3.35mins
7 Infinite repeating decimals as Geometric Series