Question 1

A geometric sequence has an initial term of 81920 and a common ratio of  0.25 . Based off of this information, what would be the sum of the first seven terms of this geometric sequence?
A) 89280
B) 92830
C) 109220
D) 123020
E) None of the above.

Accepted Answer

The answer of A geometric sequence has an initial term...

Question 2

Given that A₂₃=89 , find the value of A₂₆ given A) 733 B) 756 C) 772 D) 789 E) None of the above.

Accepted Answer

The answer of Given that A₂₃=89 , find the...

Question 3

On the initial day of class (i.e. N=0 ), a professor counts 690 students as being present in her math class. On the 6^th day of class (i.e. N=5 ) the professor counts 450 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ? A) -6 B) -18 C) -36 D) -48 E) None of the above.

Accepted Answer

The answer of On the initial day of class (i.e....

Question 4

If A_N represents the N^th term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule? A) B) C) D) E) All of the above.

Accepted Answer

The answer of If A_N represents the ...

Question 5

Given that A₂=45 and A₃=135 are the 2^nd and 3^rd terms in a geometric sequence, find A₆ . A) 3645 B) 3789 C) 3945 D) 4135 E) None of the above.

Accepted Answer

The common ratio (r) of a geometric sequence is given by the ratio of any two consecutive terms. In this case, we have:r = A3 / A2 = 135 / 45 = 3To find A6, we can use the formula for the nth term of a geometric sequence:An = A1 * r^(n-1)where A1 is the first term and n is the term number.Since we don't know A1, we can use the fact that A2 = 45 to find it:A2 = A1 * r^(2-1)45 = A1 * rA1 = 45 / rSubstituting this into the formula for An, we get:An = (45 / r) * r^(n-1)An = 45 * r^(n-2)For A6, we have n = 6, so:A6 = 45 * r^(6-2)A6 = 45 * r^4A6 = 45 * 3^4A6 = 45 * 81A6 = 3645Therefore, the correct answer is A) 3645.

Question 6

A large office building has a capacity of 14,000 people and currently 1200 have heard a juicy rumor. Assuming that the rumor spreads according to a logistic model with a growth rate of  r=3.0 , how many people does the logistic growth model predict to have heard the rumor after two transitions?
A) 4872
B) 5342
C) 6549
D) 7553
E) None of the above.

Accepted Answer

The answer of A large office building has a capacity...

Question 7

On the initial day of class (i.e. N=0 ), a professor counts 480 students as being present in her math class. On the 11^th day of class (i.e. N=10 ) the professor counts 140 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ? A) -6 B) -18 C) -34 D) -48 E) None of the above.

Accepted Answer

The answer of On the initial day of class (i.e....

Question 8

Given that A₂=35 and A₃=41 are the 2^nd and 3^rd terms an arithmetic sequence, find the term number N such that A_N=149 . A) 17 B) 21 C) 23 D) 25 E) None of the above.

Accepted Answer

The answer of Given that A₂=35 and ...

Question 9

What is the 100^th term of the sequence 3,8,13,18,23,28,..... ? A) 476 B) 498 C) 503 D) 523 E) None of the above.

Accepted Answer

The answer of What is the 100^th term...

Question 10

Jack is fascinated with sea-shells and he collects them every day on the beach. To start off with (i.e. when  N=0  ), Jack has 45 sea-shells in his collection. Each day, Jack will add 14 sea-shells to his collection. After 49 days of adding shells, how many shells in total will Jack have?
A) 731
B) 745
C) 782
D) 815
E) None of the above.

Accepted Answer

Jack has 45 sea-shells to start with, and he adds 14 sea-shells each day. After 49 days, he will have added 14 * 49 = 686 sea-shells. Therefore, he will have a total of 45 + 686 = 731 sea-shells.

Question 11

A large office building has a capacity of 15,000 people and currently 1,000 have had contact with a nasty cold virus. Assuming that the virus spreads according to a logistic model with a growth rate of  r   =3.0 , how many people does the logistic growth model predict to have come into contact with the virus after two transitions?
A) 5467
B) 6832
C) 7124
D) 8437
E) None of the above.

Accepted Answer

The answer of A large office building has a capacity...

Question 12

Given that A₃=18 and A₅=2 are the 3^rd and 5^th terms in a geometric sequence, find A₁ . A) 137 B) 143 C) 154 D) 162 E) None of the above.

Accepted Answer

In a geometric sequence, A_n = A₁ * r^(n-1). Using A₃=18 and A₅=2, we can set up the equations: A₁ * r^2 = 18 and A₁ * r^4 = 2. Dividing these gives r^2 = 1/9, so r = 1/3. Substituting back, A₁ * (1/3)^2 = 18, so A₁ = 18 * 9 = 162.

Question 13

A circular game board is shown below. The board consists of ten different regions. Half of the regions are black and half of the regions are white. Suppose that you start on one of the white regions and you move around the board clockwise. On the first region you place 3 grains of rice, on the 2^nd region you place 12 grains of rice, on the 3^rd regions you place 48 grains of rice, and so on following the pattern. You stop placing grains of rice after you reach the 10^th region. What would be the difference between the total number of grains found on white regions and the total number of grains found on black regions? A) 262144 B) 524288 C) 629145 D) 1048575 E) None of the above.

Accepted Answer

The answer of A circular game board is shown below....

Question 14

Given that A₅=46 and A₇=60 are the 5^th and 7^th terms in an arithmetic sequence, find A₃₀ . A) 176 B) 198 C) 221 D) 239 E) None of the above.

Accepted Answer

The answer of Given that A₅=46 and ...

Question 15

What is the 100^th term of the sequence 1,4,7,10,13,16,..... ? A) 264 B) 273 C) 286 D) 298 E) None of the above.

Accepted Answer

The answer of What is the 100^th term of...

Question 16

A circular game board is shown below. The board consists of ten different regions. Half of the regions are black and half of the regions are white. Suppose that you start on one of the white regions and you move around the board clockwise. On the first region you place 2 grains of rice, on the 2^nd region you place 4 grains of rice, on the 3^rd regions you place 6 grains of rice, and so on following the pattern. You stop placing grains of rice after you reach the 10^th region. What would be the difference between the total number of grains found on white regions and the total number of grains found on black regions? A) 10 B) 682 C) 1364 D) 2541 E) None of the above.

Accepted Answer

The answer of A circular game board is shown below....

Question 17

A geometric sequence has an initial term of 81920 and a common ratio of  0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?
A) 157900
B) 163800
C) 175400
D) 182500
E) None of the above.

Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio. For this sequence, a = 81920, r = 0.5, and n = 12. Plugging these values into the formula gives S_12 = 81920(1 - 0.5^12) / (1 - 0.5) = 163840(1 - 0.000244140625) = 163840 * 0.999755859375 = 163800.

Question 18

Given that A₁₁=35 Find the value of A₁₄ given A) 234 B) 286 C) 308 D) 324 E) None of the above.

Accepted Answer

The answer of Given that A₁₁=35 Find the...

Question 19

If A_N represents the N^th term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule? A) \operatorname{} B) C) D) E) None of the above.

Accepted Answer

The answer of If A_N represents the ...

Question 20

Mary is fascinated with rocks and she collects them every day at the park. To start off with (i.e. when  N=0  ), Mary has 46 rocks in her collection. Each day, Mary will add 21 new rocks to her collection. After 99 days of adding rocks, how many rocks in total will Mary have?
A) 2125
B) 2234
C) 2456
D) 2649
E) None of the above.

Accepted Answer

Mary starts with 46 rocks and adds 21 rocks each day for 99 days. So, the total number of rocks she will have is 46 + (21 * 99) = 2125.

Quiz 9: Population Growth Models: There Is Strength in Numbers

A geometric sequence has an initial term of 81920 and a common ratio of 0.25 . Based off of this information, what would be the sum of the first seven terms of this geometric sequence?

Given that A₂₃=89 , find the value of A₂₆ given

If A_N represents the N^th term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule?

Given that A₂=45 and A₃=135 are the 2^nd and 3^rd terms in a geometric sequence, find A₆ .

A large office building has a capacity of 14,000 people and currently 1200 have heard a juicy rumor. Assuming that the rumor spreads according to a logistic model with a growth rate of r=3.0 , how many people does the logistic growth model predict to have heard the rumor after two transitions?

Given that A₂=35 and A₃=41 are the 2^nd and 3^rd terms an arithmetic sequence, find the term number N such that A_N=149 .

What is the 100^th term of the sequence 3,8,13,18,23,28,..... ?

Jack is fascinated with sea-shells and he collects them every day on the beach. To start off with (i.e. when N=0 ) , Jack has 45 sea-shells in his collection. Each day, Jack will add 14 sea-shells to his collection. After 49 days of adding shells, how many shells in total will Jack have?

Given that A₃=18 and A₅=2 are the 3^rd and 5^th terms in a geometric sequence, find A₁ .

Given that A₅=46 and A₇=60 are the 5^th and 7^th terms in an arithmetic sequence, find A₃₀ .

What is the 100^th term of the sequence 1,4,7,10,13,16,..... ?

A geometric sequence has an initial term of 81920 and a common ratio of 0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?

Given that A₁₁=35 Find the value of A₁₄ given

Mary is fascinated with rocks and she collects them every day at the park. To start off with (i.e. when N=0 ) , Mary has 46 rocks in her collection. Each day, Mary will add 21 new rocks to her collection. After 99 days of adding rocks, how many rocks in total will Mary have?

Quiz 9: Population Growth Models: There Is Strength in Numbers

A geometric sequence has an initial term of 81920 and a common ratio of 0.25 . Based off of this information, what would be the sum of the first seven terms of this geometric sequence?

Given that A23=89 , find the value of A26 given

If AN represents the Nth term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule?

Given that A2=45 and A3=135 are the 2nd and 3rd terms in a geometric sequence, find A6 .