Question 1

Find the mean for the sequence of numbers.
-6, 9, 12, . . . , 129
A) 33.75
B) 67.5
C) 12
D) 39

Accepted Answer

The sequence is an arithmetic sequence with a common difference of 3, starting from 6 and ending at 129. To find the mean of the sequence, we can use the formula for the mean of an arithmetic sequence: mean = (first term + last term) / 2. Thus, mean = (6 + 129) / 2 = 135 / 2 = 67.5.

Question 2

Find the mean for the sequence of numbers.
-13 , 10 , -4 , 13 , -2
A) 6
B) 2
C) 7.5
D) 5

Accepted Answer

The answer of Find the mean for the sequence of...

Question 3

Find the mean for the sequence of numbers.
-15 , 19 , 15 , 20 , 3 , 11 , 8 , 13
A) 28
B) 12
C) 14.86
D) 13

Accepted Answer

The mean is calculated by summing all the numbers and dividing by the count of numbers: (15 + 19 + 15 + 20 + 3 + 11 + 8 + 13) / 8 = 13.

Question 4

Solve the problem.
-A town has a population of 3000 people and is increasing by 9% every year. What will the population be at the end of 9 years? Round to the nearest unit.
A) 7102 people
B) 5430 people
C) 5978 people
D) 6516 people

Accepted Answer

The answer of Solve the problem.
-A town has a population...

Question 5

Find the mean for the sequence of numbers.
-11, 7, 5, 14, 9, 3, 17
A) 
B) 
C) 
D) 10

Accepted Answer

The answer of Find the mean for the sequence of...

Question 6

Solve the problem.
-An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 735 seats
B) 600 seats
C) 1170 seats
D) 1230 seats

Accepted Answer

The number of seats in each row forms an arithmetic sequence with the first term a1 = 10 and a common difference d = 2. The nth term is given by an = a1 + (n-1)d. The total number of seats is the sum of the first 30 terms of this sequence: S30 = 30/2 * (2*10 + (30-1)*2) = 1170.

Question 7

Find the requested sum of the arithmetic sequence.
-
A) 6141
B) 6143
C) 18,865,153
D) 18,859,011

Accepted Answer

The answer of Find the requested sum of the arithmetic...

Question 8

Find the mean for the sequence of numbers.
-14 , 5 , 2 , 2 , 12
A) 6
B) 8.75
C) 7
D) 36

Accepted Answer

The mean is calculated by summing all the numbers (14 + 5 + 2 + 2 + 12 = 35) and dividing by the number of numbers (5), which equals 7.

Question 9

Find the requested sum of the arithmetic sequence.
-
A) -17
B) -14
C) 4
D) -8

Accepted Answer

The answer of Find the requested sum of the arithmetic...

Question 10

Solve the problem.
-If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 60 days?
A) $9.15
B) $0.60
C) $36.60
D) $18.30

Accepted Answer

The total amount of money is the sum of the first 60 natural numbers: 1 + 2 + 3 + ... + 60. This sum can be calculated using the formula for the sum of an arithmetic series: n(n + 1)/2, where n is the number of terms. For 60 days, the sum is 60(60 + 1)/2 = 1830 cents, which is $18.30.

Question 11

Find the requested sum of the arithmetic sequence.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the requested sum of the arithmetic...

Question 12

Find the mean for the sequence of numbers.
-4, 7, 10, 13, 16, 19, 22
A) 13
B) 16
C) 14.5
D) 29

Accepted Answer

The mean (average) is found by adding all the numbers together and dividing by the count of numbers. Here, $4 + 7 + 10 + 13 + 16 + 19 + 22 = 91$, and $91 \div 7 = 13$.

Question 13

Solve the problem.
-A woman borrowed $20,000 at 14% interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round to the nearest cent.
A) $33,779.20
B) $22,800.00
C) $31,200.00
D) $13,779.20

Accepted Answer

The amount paid off at the end of 4 years can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount, P is the principal amount ($20,000), r is the annual interest rate (14% or 0.14), and n is the number of years (4). Plugging in the values, A = 20000(1 + 0.14)^4 ≈ $33,779.20.

Question 14

Solve the problem.
-Suppose Janet could save $4 at the end of January, $8 at the end of February, $16 at the end of March, and so on. What amount would she have saved by the end of one year? Round to the nearest cent.
A) $8190.00
B) $252.00
C) $16,380.00
D) $4095.00

Accepted Answer

The answer of Solve the problem.
-Suppose Janet could save $4...

Question 15

Find the requested sum of the arithmetic sequence.
-
A) 6
B) 
C) 26
D) 77

Accepted Answer

The answer of Find the requested sum of the arithmetic...

Question 16

Solve the problem.
-A collection of dimes is arranged in a triangular array with 12 coins in the base row, 11 in the next, 10 in the next, and so forth with 1 dime in the last row. Find the value of the collection.
A) $3.90
B) $15.60
C) $0.78
D) $7.80

Accepted Answer

The total number of dimes is the sum of the first 12 natural numbers, which is calculated using the formula n(n + 1)/2, where n = 12. Thus, the total number of dimes is 12(12 + 1)/2 = 78. Since each dime is worth $0.10, the total value is 78 * $0.10 = $7.80.

Question 17

Solve the problem.
-A rose garden has 16 bushes in one row, 13 bushes in the next row, then 10, and so on. If there are 51 bushes in the garden, in how many rows are they planted?
A) 5 rows
B) 6 rows
C) 3 rows
D) 7 rows

Accepted Answer

The answer of Solve the problem.
-A rose garden has 16...

Question 18

Write out all the terms of the series.
-
A) 
B) 
C) x + 2x + 3x + 4x + 5x
D)

Accepted Answer

The answer of Write out all the terms of the...

Question 19

Find the requested sum of the arithmetic sequence.
-4, 0, -4, . . . , -156
A) -3040
B) -152
C) -156
D) -3116

Accepted Answer

The answer of Find the requested sum of the arithmetic...

Question 20

Write out all the terms of the series.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write out all the terms of the...

Quiz 11: Sequences, Series, and Probability

Find the mean for the sequence of numbers. -6, 9, 12, . . . , 129

Find the mean for the sequence of numbers. -13 , 10 , -4 , 13 , -2

Find the mean for the sequence of numbers. -15 , 19 , 15 , 20 , 3 , 11 , 8 , 13

Solve the problem. -A town has a population of 3000 people and is increasing by 9% every year. What will the population be at the end of 9 years? Round to the nearest unit.

Find the mean for the sequence of numbers. -11, 7, 5, 14, 9, 3, 17

Solve the problem. -An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Find the requested sum of the arithmetic sequence. -

Find the mean for the sequence of numbers. -14 , 5 , 2 , 2 , 12

Find the requested sum of the arithmetic sequence. -

Solve the problem. -If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 60 days?

Find the requested sum of the arithmetic sequence. -

Find the mean for the sequence of numbers. -4, 7, 10, 13, 16, 19, 22

Solve the problem. -A woman borrowed $20,000 at 14% interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round to the nearest cent.

Solve the problem. -Suppose Janet could save $4 at the end of January, $8 at the end of February, $16 at the end of March, and so on. What amount would she have saved by the end of one year? Round to the nearest cent.

Find the requested sum of the arithmetic sequence. -

Solve the problem. -A collection of dimes is arranged in a triangular array with 12 coins in the base row, 11 in the next, 10 in the next, and so forth with 1 dime in the last row. Find the value of the collection.

Solve the problem. -A rose garden has 16 bushes in one row, 13 bushes in the next row, then 10, and so on. If there are 51 bushes in the garden, in how many rows are they planted?

Write out all the terms of the series. -

Find the requested sum of the arithmetic sequence. -4, 0, -4, . . . , -156

Write out all the terms of the series. -