Question 1

If  , use mathematical induction to show that  for all positive integers n .

Accepted Answer

The answer of If  , use mathematical induction to...

Question 2

Write the first five terms of the sequence. (Assume that n begins with 1.)

Accepted Answer

A) 1, 9, 17, 25, 33 
B) -15, -22, -36, -36, -43 
C) 1, -6, -13, -20, -27 
D) 1, -14, -21, -28, -35 
E) 8, 1, -6, -13, -20

Question 3

Find the sum of the infinite geometric series below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Use the Binomial Theorem to expand and simplify the expression.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Joey bought a new tractor for use in his landscaping business. He expects that the use of the tractor will generate $ 3500 of revenue in the first year with an increase in revenue of $ 500 per year for subsequent years. If the tractor's useful lifetime is 8 years, how much revenue will Joey receive from the use of the tractor?

Accepted Answer

A) $ 7500 
B) $ 46,000 
C) $ 171,000 
D) $ 35,000 
E) $ 42,000

Question 6

Logs are stacked so that there are 24 logs in the bottom row, 23 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 five rows from the bottom?

Accepted Answer

A) 110 logs 
B) 147 logs 
C) 180 logs 
D) 129 logs 
E) 69 logs

Question 7

One card is randomly drawn from a standard deck of playing cards where aces are not considered numbered cards and are the highest card in the suit. The card is replaced and another card is drawn. What is the probability that both cards drawn are even numbered cards?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find the n th partial sum of the arithmetic sequence.  ;

Accepted Answer

A) 12 
B) -273 
C) -468 
D) 0 
E) -560

Question 9

Use the sample space defined by the experiment of tossing a fair coin four times. Express the event that there are exactly two tails as a subset of the sample space.

Accepted Answer

A) {HHHH} 
B) {TTTT, TTTH, TTHT, THTT, HTTT} 
C) {HHTT, HTHT, THHT, HTTH, THTH, TTHH} 
D) {TTTT} 
E) {HHHH, HHHT, HHTH, HTHH, THHH}

Question 10

Find the n th term of the arithmetic sequence. -1, 7, 15

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

A shipment of eleven calculators contains seven defective calculators. Four calculators are chosen from the shipment. Find the probability that exactly four are defective.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

A computer manufacturer offers a computer system with three different disk drives, three different monitors, and two different keyboards. How many different computer systems could a consumer purchase from this manufacturer?

Accepted Answer

A) 12 
B) 45 
C) 18 
D) 30 
E) 27

Question 13

To save for the replacement of a computer, a business deposits $300 at the end of each month into an account that earns 5% annual interest compounded monthly. Find the future value of the ordinary annuity in 4 years.

Accepted Answer

A) $15922.70 
B) $15936.42 
C) $15832.05 
D) $15904.47 
E) $15931.84

Question 14

Find the sixth term without expanding.

Accepted Answer

A)   
B)   
C)   
D)   
E) 252

Question 15

Find the indicated n th term of the geometric sequence. 4th term:

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Find the sum of the infinite geometric series.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if exactly four cards are aces.

Accepted Answer

A) 1,128 
B) 1,035 
C) 1,275 
D) 1,326 
E) 1,225

Question 18

Write the given series in summation notation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Evaluate the series.

Accepted Answer

A) 128 
B) 8 
C) 32 
D) 2 
E) 64

Question 20

Find the sum of the infinite geometric series.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 11: Sequences, Series, and Probability

If , use mathematical induction to show that for all positive integers n .

Write the first five terms of the sequence. (Assume that n begins with 1.)

Find the sum of the infinite geometric series below.

Use the Binomial Theorem to expand and simplify the expression.

Logs are stacked so that there are 24 logs in the bottom row, 23 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 five rows from the bottom?

One card is randomly drawn from a standard deck of playing cards where aces are not considered numbered cards and are the highest card in the suit. The card is replaced and another card is drawn. What is the probability that both cards drawn are even numbered cards?

Find the n th partial sum of the arithmetic sequence. ;

Use the sample space defined by the experiment of tossing a fair coin four times. Express the event that there are exactly two tails as a subset of the sample space.

Find the n th term of the arithmetic sequence. -1, 7, 15

A shipment of eleven calculators contains seven defective calculators. Four calculators are chosen from the shipment. Find the probability that exactly four are defective.

A computer manufacturer offers a computer system with three different disk drives, three different monitors, and two different keyboards. How many different computer systems could a consumer purchase from this manufacturer?

To save for the replacement of a computer, a business deposits $300 at the end of each month into an account that earns 5% annual interest compounded monthly. Find the future value of the ordinary annuity in 4 years.

Find the sixth term without expanding.

Find the indicated n th term of the geometric sequence. 4th term:

Find the sum of the infinite geometric series.

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if exactly four cards are aces.

Write the given series in summation notation.

Evaluate the series.

Find the sum of the infinite geometric series.