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

1 + 10 + 100 + ...

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

6 + 12 + 18 + 24 + ...

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

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

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

7 - 8 - 10 - 13 - ...

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

6571 - 2187 + 729 - 243 + ...

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

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

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

S_9 for 3 + 6 + 12 + ...

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

S_12 for 5 - 10 + 20 - ...

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} + ...

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 + ...

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

S_50 for 9 - 9 + 9 - ...

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

S_17 for 2 + 0.2 + 0.02 + ...

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

a = 16, r = 2, n = 13

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

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

Determine S_n for each geometric series.

a = 20, r = 6, n = 5

Determine the sum of each geometric series.

1 + 5 + 25 + ... + 3125

Determine the sum of each geometric series.

3 + 9 + 27 + ... + 59049

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

5 + 20 + 80 + ... + 20480

Determine the sum of each geometric series.

Determine the sum of each geometric series.

2700 + 270 + 27 + ... + 0.0027

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

3 + 9 + 27 + ... + 6561

Determine the sum of each geometric series.

100 + 25 + 6.25 + ... + 0.390625

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

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

Determine the specified sum for each geometric series.

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

Determine the specified sum for each geometric series.

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

Determine the specified sum for each geometric series.

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

Determine the specified sum for each geometric series.

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

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

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

Determine the sum of each geometric series.

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

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}

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}

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}

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

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

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}.

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.

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?

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.

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.

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

Determine the sum of the factors of 3^8.

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.