6.7 Geometric Series
Chapter
Chapter 6
Section
6.7
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Lectures 4 Videos

Finding the General Term and the 15th Term for Geometric Sequence

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Finding the General Term and the 15th Term for Geometric Sequence

Given three consecutive terms in geometric sequence finding the general term

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Given three consecutive terms in geometric sequence finding the general term
Solutions 54 Videos

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

1 + 10 + 100 + ...

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Q1a

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

6 + 12 + 18 + 24 + ...

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Q1b

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

-4 + 8 - 16 + 32 - ...

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Q1c

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

7 - 8 - 10 - 13 - ...

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Q1d

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

6571 - 2187 + 729 - 243 + ...

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Q1e

Determine whether each series is geometric, arithmetic, or neither. Justify your answer.

\dfrac{1}{8} + \dfrac{1}{7} + \dfrac{1}{6} + \dfrac{1}{5} + ...

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Q1f

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_9 for 3 + 6 + 12 + ...

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Q2a

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_12 for 5 - 10 + 20 - ...

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Q2b

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_8 for \dfrac{1}{8} + \dfrac{1}{4} + \dfrac{1}{2} + ...

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Q2c

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_13 for -0.2 + 0.6 - 1.8 + ...

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Q2d

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_50 for 9 - 9 + 9 - ...

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Q2e

For each geometric series. determine the values of a and r. Then. determine the specified sum.

S_17 for 2 + 0.2 + 0.02 + ...

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Q2f

Determine S_n for each geometric series.

a = \dfrac{1}{81}, r = 3, n = 7

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Q3a

Determine S_n for each geometric series.

f(1) = 6, r = -\dfrac{1}{2}, n = 11

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Q3b

Determine S_n for each geometric series.

f(1) = 4, r = -2, n = 10

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Q3c

Determine S_n for each geometric series.

f(1) = -6, r = 4, n = 9

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Q3d

Determine S_n for each geometric series.

a = 16, r = 2, n = 13

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Q3e

Determine S_n for each geometric series.

a = -2, r = 2, n = 13

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Q3f

Determine S_n for each geometric series.

f(1) = 0.4, r = 1.5, n = 6

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Q3g

Determine S_n for each geometric series.

a = -4, r = -1, n = 20

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Q3h

Determine S_n for each geometric series.

a = 20, r = 6, n = 5

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Q3i

Determine the sum of each geometric series.

1 + 5 + 25 + ... + 3125

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Q4a

Determine the sum of each geometric series.

3 + 9 + 27 + ... + 59049

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Q4b

Determine the sum of each geometric series.

\dfrac{1}{3} + 1 + 3 + ... + 6561

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Q4c

Determine the sum of each geometric series.

5 + 20 + 80 + ... + 20480

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Q4d

Determine the sum of each geometric series.

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Q4e

Determine the sum of each geometric series.

2700 + 270 + 27 + ... + 0.0027

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Q4f

Determine the sum of each geometric series.

243 + 81 + 27 + ... + \dfrac{1}{27}

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Q4g

Determine the sum of each geometric series.

2 + 1 + \dfrac{1}{2} + ... + \dfrac{1}{128}

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Q5a

Determine the sum of each geometric series.

3 + 9 + 27 + ... + 6561

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Q5b

Determine the sum of each geometric series.

100 + 25 + 6.25 + ... + 0.390625

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Q5c

Determine the sum of each geometric series.

5 + \dfrac{5}{2} + \dfrac{5}{4} + ... + \dfrac{5}{512}

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Q5d

Determine the sum of each geometric series.

5 - \dfrac{5}{2} + \dfrac{5}{4} - ... - \dfrac{5}{512}

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Q5e

Determine the specified sum for each geometric series.

S_8 for \sqrt{5} - 5 + 5\sqrt{5} - ...

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Q6a

Determine the specified sum for each geometric series.

S_13 for x + x\sqrt{7} + 7x + 7\sqrt{7}x + ...

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Q6b

Determine the specified sum for each geometric series.

S_14 for 4 + 4x + 4x^2 + ...

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Q6c

Determine the specified sum for each geometric series.

S_11 for 2 + 2x^2 + 2x^4 + ...

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Q6d

Determine the sum of each geometric series.

1 + \dfrac{5}{2} + \dfrac{25}{2} + ... + \dfrac{15625}{64}

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Q7a

Determine the sum of each geometric series.

3\sqrt{6} - 18 + 18\sqrt{6} - ... + 839808\sqrt{6}

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Q7b

Determine the sum of each geometric series.

500 + 500(1.2) + 500(1.2)^2 + ... + 500(1.2)^{11}

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Q7c

Determine the sum of each geometric series.

8 + 16x^3 + 32x^6 + ... + 32768x^36

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Q7d

Find an expression for the sum of the first n terms of the series with the given general term. Then, use your expression to find the sum when n = 9.

t_n = -2(3)^{n-1}

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Q8a

Find an expression for the sum of the first n terms of the series with the given general term. Then, use your expression to find the sum when n = 9.

t_n = 18(\dfrac{2}{3})^{n-1}

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Q8b

Find an expression for the sum of the first n terms of the series with the given general term. Then, use your expression to find the sum when n = 9.

t_n = x^2(x^2)^{n-1}

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Q8c

Determine the sum of the first 10 terms of a geometric series with common ratio 2 and whose tenth term is 16.

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Q9

The sum of the first seven terms of a geometric series is 70 993 and the common ratio is 4. Determine the first term.

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Q10

Determine the fourth term of a geometric series given that the sum of the first seven terms of the series is 1093 and the common ratio is 3^{-1}.

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Q11

Tatiana is training for a marathon that will take place in four months. This week ‘ she ran 45 km and intends to increase her distance by 10% each week. Determine the total distance that Tatiana will have run after 10 weeks.

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Q12

In a lottery, the first ticket drawn wins a prize of $25, the second ticket drawn receives a prize of $75, the third ticket drawn receives a prize of $225, and so on. How many prizes can be given out if the total amount of prize money is $1 million?

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Q13

Kayla tried to convince her dad that during the month of April, he should pay her allowance in the following manner: 1 penny on the first day of the month, 2 pennies on the second day of the month, 4 pennies on the third day, 8 pennies on the fourth day, and so on until the last day of the month. What is the total allowance Kayla would receive if her dad agrees to her idea? Do you think he will agree? Explain.

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Q14

If the second term of a geometric series is 15 and the sum of the first three terms is 93, determine the general term of the series.

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Q15

Show that the sum of 4 + 2 + 1+ 0.5 + 0.25+ ... + t_n is always less than 8 for any natural number n.

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Q16

Determine the sum of the factors of 3^8.

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Q17

a) Determine an expression for the sum of the first n terms of a series with general term t_n = 2^n - 3^{n-1}.
b) Use your expression from part a) to find the sum of the first six terms of the series with the given general term.

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Q18