Question 1

Find the sum of the infinite geometric series.
​

Accepted Answer

The answer of Find the sum of the infinite geometric...

Question 2

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
27, 64, 125, 216, ...
​

Accepted Answer

The sequence consists of cubes of natural numbers (3^3, 4^3, 5^3, 6^3, ...), so the next term is 7^3 = 343. It does not fit the definition of arithmetic, geometric, or Fibonacci sequences.

Question 3

Find the sum of the even integers between 51 and 99. ​

Accepted Answer

The even integers between 51 and 99 are 52, 54, ..., 98. This is an arithmetic sequence with the first term $a = 52$, the last term $l = 98$, and the common difference $d = 2$. To find the sum, we first need to find the number of terms $n$. Since the sequence is even numbers, we can calculate $n$ as $\frac{98 - 52}{2} + 1 = 24$. The sum of an arithmetic sequence is given by $S = \frac{n}{2}(a + l)$, substituting the values gives $S = \frac{24}{2}(52 + 98) = 12 \times 150 = 1800$.

Question 4

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
1, 6, 7, 13, ...
​

Accepted Answer

The sequence follows the Fibonacci pattern, where each term is the sum of the two preceding ones (1+6=7, 6+7=13), making the next term 20 (7+13=20).

Question 5

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
3, 4, 5, 6, ...
​

Accepted Answer

The sequence is arithmetic because each term increases by a constant difference of 1. The next term after 6 is 7.

Question 6

A tennis ball is dropped from a height of 15 ft. If the ball rebounds  of its height on each bounce, how far will the ball travel before coming to rest? ​​

Accepted Answer

The total distance the ball travels is calculated by adding up the distance it travels during each bounce. The ball rebounds 11/15 of its height, so after the first bounce, it reaches a height of 11/15*15 = 11 ft. It then falls from 11 ft to the ground, for a total distance of 11 ft + 15 ft = 26 ft traveled on the first bounce. On the second bounce, the ball rebounds 11/15*11 = 8.14 ft, and falls from 8.14 ft to the ground, for a total distance of 8.14 ft + 11 ft = 19.14 ft traveled on the second bounce. On the third bounce, the ball rebounds 11/15*8.14 = 5.89 ft, and falls from 5.89 ft to the ground, for a total distance of 5.89 ft + 8.14 ft = 13.03 ft traveled on the third bounce. The ball will then bounce again, but not rise high enough to count as a bounce, and come to rest. Adding up the distances traveled, we get 26 ft + 19.14 ft + 13.03 ft = 58.17 ft, which is closest to answer choice B, 75 ft.

Question 7

Evaluate the expression
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Accepted Answer

The answer of Evaluate the expression
​ ...

Question 8

Find the sum of the first 19 positive integers.

Accepted Answer

The answer of Find the sum of the first 19...

Question 9

The game of pool uses 15 balls numbered from 1 to 15 (see the figure below). In the game of rotation, a player attempts to "sink" a ball in a pocket of the table and receives the number of points on the ball. Suppose we consider a game of "super pool", which has 19 consecutively numbered balls on the table. How many points would a player receive to "run the table"? ​  ​

Accepted Answer

The answer of The game of pool uses 15 balls...

Question 10

A tennis ball is dropped from a height of 13 ft. If the ball rebounds  of its height on each bounce, how far will the ball travel before coming to rest?
​
__________ ft

Accepted Answer

The answer of A tennis ball is dropped from a...

Question 11

Evaluate the expression.
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Accepted Answer

The answer of Evaluate the expression.
​ ...

Question 12

Find ​  when
​  ​  __________

Accepted Answer

The answer of Find ​  when
​  ​ ...

Question 13

Find the sum of the even integers between 49 and 101.

Accepted Answer

The answer of Find the sum of the even integers...

Question 14

Find the first three terms of the sequence whose nth term is given. ​  ​

Accepted Answer

The given nth term has a pattern where the last four digits increase by one in each term. Therefore, the first three terms must have the same first eight digits and the last four digits should increase by one in each term. Only option C satisfies this pattern.

Question 15

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​
3, 15, 75, 375, ...
​

Accepted Answer

The sequence is increasing, so it cannot be arithmetic or Fibonacci. The common ratio is 5, so it is geometric. The next term would be 1875.

Question 16

Find the first three terms of the sequence whose nth term is given. ​  ​

Accepted Answer

The answer of Find the first three terms of the...

Question 17

Find  when
​  ​  __________

Accepted Answer

The answer of Find  when
​  ​  __________...

Question 18

The game of pool uses 15 balls numbered from 1 to 15 (see the figure below). In the game of rotation, a player attempts to "sink" a ball in a pocket of the table and receives the number of points on the ball. Suppose we consider a game of "super pool", which has 15 consecutively numbered balls on the table. How many points would a player receive to "run the table"?
​  ​
__________ points

Accepted Answer

The answer of The game of pool uses 15 balls...

Question 19

Evaluate the expression.
​

Accepted Answer

The answer of Evaluate the expression.
​ ...

Question 20

Find the sum of the first 12 positive integers. ​

Accepted Answer

The answer of Find the sum of the first 12...

Quiz 11: The Nature of Sequences, Series, and Financial Management

Find the sum of the infinite geometric series.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 27, 64, 125, 216, ...

Find the sum of the even integers between 51 and 99.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 1, 6, 7, 13, ...

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 3, 4, 5, 6, ...

A tennis ball is dropped from a height of 15 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest?

Evaluate the expression

Find the sum of the first 19 positive integers.

A tennis ball is dropped from a height of 13 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest? __________ ft

Evaluate the expression.

Find when __________

Find the sum of the even integers between 49 and 101.

Find the first three terms of the sequence whose nth term is given.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 3, 15, 75, 375, ...

Find the first three terms of the sequence whose nth term is given.

Find when __________

Evaluate the expression.

Find the sum of the first 12 positive integers.

Quiz 11: The Nature of Sequences, Series, and Financial Management

Find the sum of the infinite geometric series. ​

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​ 27, 64, 125, 216, ... ​

Find the sum of the even integers between 51 and 99. ​

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​ 1, 6, 7, 13, ... ​

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​ 3, 4, 5, 6, ... ​

A tennis ball is dropped from a height of 15 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest? ​​

Evaluate the expression ​

Find the sum of the first 19 positive integers.

A tennis ball is dropped from a height of 13 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest? ​ __________ ft

Evaluate the expression. ​

Find ​ when ​ ​ __________

Find the sum of the even integers between 49 and 101.

Find the first three terms of the sequence whose nth term is given. ​ ​

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. ​ 3, 15, 75, 375, ... ​

Find the first three terms of the sequence whose nth term is given. ​ ​

Find when ​ ​ __________

Evaluate the expression. ​

Find the sum of the first 12 positive integers. ​

Find the sum of the infinite geometric series.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 27, 64, 125, 216, ...

Find the sum of the even integers between 51 and 99.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 1, 6, 7, 13, ...

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 3, 4, 5, 6, ...

A tennis ball is dropped from a height of 15 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest?

Evaluate the expression

A tennis ball is dropped from a height of 13 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest? __________ ft

Evaluate the expression.

Find when __________

Find the first three terms of the sequence whose nth term is given.

Classify the sequence as arithmetic, geometric, Fibonacci, or none of these and supply the next term. 3, 15, 75, 375, ...

Find the first three terms of the sequence whose nth term is given.

Find when __________

Evaluate the expression.

Find the sum of the first 12 positive integers.