Question 1

The seating section in a theater has 24 seats in the first row, 27 seats in the second row, and so on, increasing by 3 seats each row for a total of 19 rows.How many seats are in the tenth row?
A) 
B) 
C) 
D) 
E)

Accepted Answer

To find the number of seats in the nth row, we can use the formula n + (n-1)x3, where n is the row number. 
So for the 10th row, we have 10 + (10-1)x3 = 10 + 27 = 37 seats. 
Therefore, the answer is choice B.

Question 2

Logs are stacked so that there are 21 logs in the bottom row, 20 logs in the second row from the bottom, and so on, decreasing by 1 log each row.How many logs are there in the first four rows from the bottom?
A) 140 logs
B) 60 logs
C) 78 logs
D) 153 logs
E) 165 logs

Accepted Answer

We can use a simple arithmetic series formula to find the total number of logs in the first four rows:
Total = (n/2) x (a + l)
where n is the number of terms, a is the first term, l is the last term, and all terms are added together.
In this case, n = 4 (since we want the first four rows), a = 21 (the first row has 21 logs), and l = 18 (the fourth row has 18 logs). 
Plugging these values into the formula, we get:
Total = (4/2) x (21 + 18) = 2 x 39 = 78
Therefore, there are 78 logs in the first four rows from the bottom. So, the best choice is (C).

Question 3

Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.
A) $366,700
B) $312,725
C) $77,725
D) $423,000
E) $120,075

Accepted Answer

The total compensation over three years is calculated by summing the starting salary and the raises for each year: $37,700 + ($37,700 + $2,325) + ($37,700 + 2*$2,325) = $120,075.

Question 4

Use summation notation to write the sum below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use summation notation to write the sum...

Question 5

Find the nth term of the geometric sequence. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the nth term of the geometric...

Question 6

Find a formula for  for the arithmetic sequence below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a formula for  for the...

Question 7

Write the first five terms of the geometric sequence. 
A) -5, -2, 1, 4, 7
B) -5, -15, -45, -135, -405
C) 
D) 
E)

Accepted Answer

The answer of Write the first five terms of the...

Question 8

Find the nth term of the geometric sequence. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the nth term of the geometric...

Question 9

Match the geometric sequence with its graph from the choices below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Match the geometric sequence with its graph...

Question 10

Determine whether the sequence is geometric.If so, find the common ratio. -5, -15, -45, -135, ...
A) 3
B) -5
C) 
D) -3
E) not geometric

Accepted Answer

The answer of Determine whether the sequence is geometric.If so,...

Question 11

Find the sum of the integers from 31 to 61.
A) 1891
B) 30
C) 2852
D) 1426
E) 3782

Accepted Answer

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

Question 12

Match the arithmetic sequence with its graph from the choices below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Match the arithmetic sequence with its graph...

Question 13

Write the first five terms of the arithmetic sequence. 
A) 3, 10, 17, 24, 31
B) -4, -11, -18, -25, -32
C) 3, -4, -11, -18, -25
D) 3, -21, 147, -1029, 7203
E) 3, -4, -1, 2, 5

Accepted Answer

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed number (called the common difference) to the preceding term. Looking at the options, only option C has a common difference of -7. Therefore, the first five terms of the arithmetic sequence would be: 3, -4, -11, -18, -25.

Question 14

Find the partial sum. 
A) -100,098
B) -99,102
C) -100,900
D) -101,103
E) -100,100

Accepted Answer

The answer of Find the partial sum. 
A) -100,098
B) -99,102
C)...

Question 15

A heavy object (with negligible air resistance) is dropped from a plane.During the first second of fall, the object falls 16.6 meters; during the second second, it falls 49.8 meters; during the third second, it falls 83.0 meters; and during the fourth second, it falls 116.2 meters.If this pattern continues, how many meters will the object fall in 10 seconds?
A) 813.4 meters
B) 597.6 meters
C) 1062.4 meters
D) 1660.0 meters
E) 1344.6 meters

Accepted Answer

The answer of A heavy object (with negligible air resistance)...

Question 16

Find the indicated nth partial sum of the arithmetic sequence. 2.5, 3.8, 5.1, 6.4, ..., n = 100
A) 12,505
B) 6815
C) 6685
D) 6683.8
E) 6686.2

Accepted Answer

The sequence is arithmetic with the first term a = 2.5 and common difference d = 1.3. The nth partial sum of an arithmetic sequence is given by S_n = n/2 * (2a + (n-1)d). Substituting n = 100, a = 2.5, and d = 1.3, we get S_100 = 100/2 * (2*2.5 + 99*1.3) = 6685.

Question 17

Determine whether the sequence is geometric.If so, find the common ratio. -5, -2, 1, 4, ...
A) 3
B) -5
C) 
D) -3
E) not geometric

Accepted Answer

The answer of Determine whether the sequence is geometric.If so,...

Question 18

Find the indicated nth term of the geometric sequence. 6th term: 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indicated nth term of the...

Question 19

The annual sales  (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model   where  represents the year, with  corresponding to 2001.Find the total sales from 2001 to 2005.Round to the nearest million.
A) $4119 million
B) $5427 million
C) $2972 million
D) $3295 million
E) $2003 million

Accepted Answer

The answer of The annual sales  (in millions of...

Question 20

Use a graphing utility to graph the first 10 terms of the sequence. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using a graphing utility, we can easily graph the first 10 terms of the sequence. Choosing the other answer choices would result in graphs that do not represent the sequence given. The graph of choice B correctly shows that the terms of the sequence are increasing exponentially.

Quiz 7: Sequences, Series, and Probability

The seating section in a theater has 24 seats in the first row, 27 seats in the second row, and so on, increasing by 3 seats each row for a total of 19 rows.How many seats are in the tenth row?

Logs are stacked so that there are 21 logs in the bottom row, 20 logs in the second row from the bottom, and so on, decreasing by 1 log each row.How many logs are there in the first four rows from the bottom?

Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.

Use summation notation to write the sum below.

Find the nth term of the geometric sequence.

Find a formula for for the arithmetic sequence below.

Write the first five terms of the geometric sequence.

Find the nth term of the geometric sequence.

Match the geometric sequence with its graph from the choices below.

Determine whether the sequence is geometric.If so, find the common ratio. -5, -15, -45, -135, ...

Find the sum of the integers from 31 to 61.

Match the arithmetic sequence with its graph from the choices below.

Write the first five terms of the arithmetic sequence.

Find the partial sum.

Find the indicated nth partial sum of the arithmetic sequence. 2.5, 3.8, 5.1, 6.4, ..., n = 100

Determine whether the sequence is geometric.If so, find the common ratio. -5, -2, 1, 4, ...

Find the indicated nth term of the geometric sequence. 6th term:

The annual sales (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001.Find the total sales from 2001 to 2005.Round to the nearest million.

Use a graphing utility to graph the first 10 terms of the sequence.