Question 1

Solve.
-For the geometric sequence 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve.
-For the geometric sequence 
A) 
B) 
C)...

Question 2

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-7, -14, 28, -56, 112, ...
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 3

Solve.
-Find the 10th term of the geometric sequence  .
A)6561
B)19683
C)2187
D)177,147

Accepted Answer

The answer of Solve.
-Find the 10th term of the geometric...

Question 4

Find the sum.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the sum.
-
A) 
B) 
C) 
D) ...

Question 5

Solve.
-A particular substance decays in such a way that it loses half its weight each day. How much of thesubstance is left after 9 days if it starts out at 64 grams?
A)  gram
B)8 grams
C)  gram
D)4 grams

Accepted Answer

The answer of Solve.
-A particular substance decays in such a...

Question 6

Solve.
-For the geometric sequence 64, 16, 4, 1, ... , find a 
A) 
B) 
C) 
D)

Accepted Answer

The given sequence is a geometric sequence with a common ratio of $\frac{1}{4}$. To find the 11th term, we can use the formula $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Plugging in, we get:
$$a_{11} = 64 \cdot \left(\frac{1}{4}\right)^{10} = \frac{64}{4^{10}} = \frac{64}{2^{20}}$$
Simplifying, we get:
$$\frac{64}{2^{20}} = \frac{2^6}{2^{20}} = 2^{-14}$$
Converting to scientific notation, we get $2^{-14} = 1.52587890625 \cdot 10^{-5}$. Therefore, the 11th term is approximately $1.52587890625 \cdot 10^{-5}$.
Since only choice A is equal to $1.52587890625 \cdot 10^{-5}$, it must be the correct answer.

Question 7

Solve.
-A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swingsonly 66% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answerto two decimal places, if necessary.
A)2.88 inches
B)1.9 inches
C)1.25 inches
D)422.4 inches

Accepted Answer

The length of the arc after 9 swings can be found using the formula for the nth term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 80$ inches, $r = 0.66$, and $n = 9$. So, $a_9 = 80 \cdot 0.66^{(9-1)} = 80 \cdot 0.66^8 \approx 2.88$ inches.

Question 8

Solve.
-Carla takes a job with a starting salary of $42,000 for the first year with an annual increase of 6% beginningin the second year. What is Carlaʹs salary, to the nearest dollar, in the sixth year?
A)$56,205
B)$56,788
C)$54,783
D)$58,307

Accepted Answer

Carla's salary in the sixth year can be calculated using the formula for the future value of a series with annual compounding: $FV = P(1 + r)^n$, where $P$ is the principal amount ($42,000), $r$ is the annual increase rate (6% or 0.06), and $n$ is the number of years (5 years, since the increase starts in the second year). Plugging in the values: $FV = 42000(1 + 0.06)^5 = 42000(1.338225577)$, which gives approximately $56,205, rounded to the nearest dollar.

Question 9

Solve.
-A new piece of equipment cost a company $45,000. Each year, for tax purposes, the company depreciatesthe value by 25%.What value should the company give the equipment after 6 years?
A)$8,009
B)$11
C)$10,679
D)$44

Accepted Answer

The value of the equipment after 6 years is $10,679. This is because the equipment depreciates by 25% each year, so after 6 years, the value of the equipment is 25% of its original value. 25% of $45,000 is $10,679.

Question 10

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 11

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 12

Find the sum.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the sum.
-
A) 
B) 
C) 
D) ...

Question 13

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-
A) 
B) 
C) 
D)a

Accepted Answer

The answer of Find the nth term {an} of the...

Question 14

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-4 + 12 + 36 + 108 + 324 + ... + 
A)13,120
B)13,100
C)13,157
D)13,122

Accepted Answer

The answer of Use a graphing utility to find the...

Question 15

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-2, 4, 8, 16, 32, ...
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 16

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
--6, -12, -24, -48, -96, ...
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 17

Solve.
-A basketball player signs a contract with a starting salary of $850,000 per year and an annual increase of6.5% beginning in the second year. What will the athleteʹs salary be, to the nearest dollar, in the sixth year?
A)$1,164,574
B)$1,165,367
C)$1,163,330
D)$1,166,854

Accepted Answer

The salary in the sixth year can be calculated using the formula for the amount in a geometric sequence, $A = P(1 + r)^n$, where $P$ is the initial amount, $r$ is the rate of increase (expressed as a decimal), and $n$ is the number of periods. Here, $P = \$850,000$, $r = 0.065$, and $n = 5$ (since the increase starts in the second year, the sixth year is the fifth year of increase). Plugging these values in, we get $A = 850,000(1 + 0.065)^5$, which calculates to approximately \$1,164,574.

Question 18

Find the sum.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the sum.
-
A) 
B) 
C) 
D) ...

Question 19

Find the sum.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the sum.
-
A) 
B) 
C) 
D) ...

Question 20

Solve.
-A bicycle wheel rotates 400 times in a minute as long as the rider is pedaling. If the rider stops pedaling,the wheel starts to slow down. Each minute it will rotate only  as many times as in the precedingminute. How many times will the wheel rotate in the 5th minute after the riderʹs feet leave the pedals?Round your answer to the nearest unit.
A)95 times
B)127 times
C)0 times
D)2 times

Accepted Answer

The answer of Solve.
-A bicycle wheel rotates 400 times in...

Quiz 9: Sequences; Induction; the Binomial Theorem

Solve. -For the geometric sequence

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -7, -14, 28, -56, 112, ...

Solve. -Find the 10th term of the geometric sequence .

Find the sum. -

Solve. -A particular substance decays in such a way that it loses half its weight each day. How much of thesubstance is left after 9 days if it starts out at 64 grams?

Solve. -For the geometric sequence 64, 16, 4, 1, ... , find a

Solve. -A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swingsonly 66% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answerto two decimal places, if necessary.

Solve. -Carla takes a job with a starting salary of $42,000 for the first year with an annual increase of 6% beginningin the second year. What is Carlaʹs salary, to the nearest dollar, in the sixth year?

Solve. -A new piece of equipment cost a company $45,000. Each year, for tax purposes, the company depreciatesthe value by 25%.What value should the company give the equipment after 6 years?

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -

Find the sum. -

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -4 + 12 + 36 + 108 + 324 + ... +

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -2, 4, 8, 16, 32, ...

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. --6, -12, -24, -48, -96, ...

Solve. -A basketball player signs a contract with a starting salary of $850,000 per year and an annual increase of6.5% beginning in the second year. What will the athleteʹs salary be, to the nearest dollar, in the sixth year?

Find the sum. -

Find the sum. -