Deck 10: Sequences, Series and the Binomial Theorem

Question 1

Evaluate:

A) 5060
B) 24
C) 266
D) 276
E) None of these

Answer 1

276

Question 2

A) 120
B) 0
C) 1
D) undefined
E) None of these

Answer 2

120

Question 3

Do not use Pascal's Triangle.

-Evaluate:

A) 20
B) 110
C) 40
D) 55
E) None of these

Answer 3

55

Question 4

Do not use Pascal's Triangle.

-Evaluate:

A) 290
B) 280
C) 310
D) 300
E) None of these

Question 5

Do not use Pascal's Triangle.

-Find the coefficient of the sixth term of the binomial expansion of

A) 253
B) 251
C) 252
D) 20
E) None of these

Question 6

Do not use Pascal's Triangle.

-Find the coefficient of the 9th term in the binomial expansion of

A) 6435
B) 5005
C) 1716
D) 135
E) None of these

Question 7

Do not use Pascal's Triangle.

-Identify the number of terms in the expansion of

A) 27
B) 54
C) 26
D) 28
E) None of these

Question 8

Expand the expression. Use Pascal's Triangle to find the coefficients and use the binomial theorem to find the variables in each term.

-

A)
B)
C)
D)
E) None of these

Question 9

Expand the expression. Use Pascal's Triangle to find the coefficients and use the binomial theorem to find the variables in each term.

-

A)
B)
C)
D)
E) None of these

Question 10

Expand the expression. Use Pascal's Triangle to find the coefficients and use the binomial theorem to find the variables in each term.

-

A)
B)
C)
D)
E) None of the above

Question 11

Expand the expression. Use Pascal's Triangle to find the coefficients and use the binomial theorem to find the variables in each term.

-

A)
B)
C)
D)
E) None of the above

Question 12

Use Pascal's Triangle and the binomial theorem to find the 3rd term in the expansion of

A)
B)
C)
D)
E) None of these

Question 13

Use Pascal's Triangle and the binomial theorem to find the 8th term in the expansion of

A)
B)
C)
D)
E) None of these

Question 14

The expression is equivalent to . Expand this expression using Pascal's Triangle and the binomial theorem to find the sum of the terms.

A) 6.55
B) 10.4641
C) 1.4641
D) 1.0001
E) None of these

Question 15

Find the common ratio, r, of the given geometric sequence.

-

A) 20
B) 10
C) 5
D) 40
E) None of these

Question 16

Find the common ratio, r, of the given geometric sequence.

-

A)
B)
C)
D)
E) None of these

Question 17

Find the common ratio, r, of the given geometric sequence.

-

A)
B)
C)
D)
E) None of these

Question 18

Which of the following sequences is geometric?

A)
B)
C)
D)
E) None of these

Question 19

The seventh term of a geometric sequence is . The common ratio is .

-Find the eighth term of the sequence.

A) 729
B) - 2187
C) -729
D) 2187
E) None of these

Question 20

The seventh term of a geometric sequence is . The common ratio is .

-Find a formula for the nth term of the sequence.

A)
B)
C)
D)
E) None of these

Question 21

The tenth term in a geometric sequence is 1,000,000,000. The common ratio is 10.

-Find the 11th term of the sequence.

A) 100,000,000
B) 10,000,000,000
C) 1,000,000,010
D) 999,999,990
E) None of these

Question 22

The tenth term in a geometric sequence is 1,000,000,000. The common ratio is 10.

-Find a formula for the nth term of the seqence.

A)
B)
C)
D)
E) None of these

Question 23

Evaluate the partial sum of the geometric series.

-

A) -513
B) 508
C) 513
D)-508
E) None of these

Question 24

Evaluate the partial sum of the geometric series.

-; six terms.

A) 2912
B) 1456
C) 1458
D) 2914
E) None of these

Question 25

Evaluate the partial sum of the geometric series.

-; five terms

A)
B) 30
C)
D)
E) None of these

Question 26

Evaluate the infinite geometric series.

-

A) 24
B) 30
C) 15
D) 3
E) None of these

Question 27

Evaluate the infinite geometric series.

-

A)
B)
C)
D)
E) None of these

Question 28

Evaluate the infinite geometric series.

-

A) 1000
B) 500
C) 250
D) 100
E) None of these

Question 29

The function is a model of the number of units sold each year of a product, , when the number of years since 2006 in t. Rewrite the function as a geometric sequence with a domain of . Round to the nearest whole number.

A)
B)
C)
D)
E) None of these

Question 30

For all the problems in this set the domain is the set of positive integers.

-Find the common difference, d, of the arithmetic sequence )

A) 3
B) 4
C) -3
D) 5
E) None of these

Question 31

For all the problems in this set the domain is the set of positive integers.
Find a formula for the nth term of the arithmetic sequence.

-

A)
B)
C)
D)
E) None of these

Question 32

For all the problems in this set the domain is the set of positive integers.
Find a formula for the nth term of the arithmetic sequence.

-

A)
B)
C)
D)
E) None of these

Question 33

For all the problems in this set the domain is the set of positive integers.
Find a formula for the nth term of the arithmetic sequence.

-

A)
B)
C)
D)
E) None of these

Question 34

For all the problems in this set the domain is the set of positive integers.

-Which of the following sequences, if any, is an arithmetic sequence?

A)
B)
C)
D)
E) None of these

Question 35

For all the problems in this set the domain is the set of positive integers.

-The 10th term in an arithmetic sequence is 45. The common difference is 15. Find the 11th term in this sequence.

A) 50
B) 30
C) 58
D) 60
E) None of these

Question 36

For all the problems in this set the domain is the set of positive integers.
Each of the sequences is arithmetic. Find the formula for the nth term.

-The 12th term is 156. The common difference is 12.

A)
B)
C)
D)
E) None of these

Question 37

For all the problems in this set the domain is the set of positive integers.
Each of the sequences is arithmetic. Find the formula for the nth term.

-The 3rd term is 29. The 7th term is 57.

A)
B)
C)
D)
E) None of these

Question 38

For all the problems in this set the domain is the set of positive integers.
Each of the sequences is arithmetic. Find the formula for the nth term.

-The 6th term is . The common difference is .

A)
B)
C)
D)
E) None of these

Question 39

For all the problems in this set the domain is the set of positive integers.
Evaluate the partial sum of the given number of terms of the arithmetic sequence.

-; the first 18 terms.

A) -54
B) 273
C) 252
D) 306
E) None of these

Question 40

For all the problems in this set the domain is the set of positive integers.
Evaluate the partial sum of the given number of terms of the arithmetic sequence.

-; the first 40 terms.

A) 7200
B) 7800
C) 8800
D) 7000
E) None of these

Question 41

For all the problems in this set the domain is the set of positive integers.
Evaluate the partial sum of the given number of terms of the arithmetic sequence.

-Evaluate the sum of the first 50 integers greater than zero.

A) 1275
B) 1300
C) 1375
D) 1250
E) None of these

Question 42

For all the problems in this set the domain is the set of positive integers.

-Evaluate the sum of the first 50 odd integers greater than zero.

A) 1200
B) 1250
C) 1225
D) 2500
E) None of these

Question 43

For all the problems in this set the domain is the set of positive integers.

-The first row in an auditorium has 10 seats. Each successive row has 4 more seats. Use a partial sum to find the total number of seats in the first 20 rows.

A) 400
B) 1240
C) 960
D) 840
E) None of these

Question 44

For all the problems in this set the domain is the set of positive integers.

-The bottom row of a stack of cans contains 35 cans. Each layer contains one fewer can than the layer below it. The top row has 1 can. How many cans are in the stack?

A) 630
B) 612
C) 595
D) 578
E) None of these

Question 45

For all the problems in this set the domain is the set of positive integers greater than 0.
Use roster notation to represent the range of the sequence.

-

A)
B)
C)
D)
E) None of these

Question 46

For all the problems in this set the domain is the set of positive integers greater than 0.
Use roster notation to represent the range of the sequence.

-

A)
B)
C)
D)
E) None of these

Question 47

For all the problems in this set the domain is the set of positive integers greater than 0.
Use roster notation to represent the range of the sequence.

-

A)
B)
C)
D)
E) None of these

Question 48

For all the problems in this set the domain is the set of positive integers greater than 0.
Find a formula for the nth term of each sequence.

-

A)
B)
C)
D)
E) None of these

Question 49

For all the problems in this set the domain is the set of positive integers greater than 0.
Find a formula for the nth term of each sequence.

-

A)
B)
C)
D)
E) None of these

Question 50

For all the problems in this set the domain is the set of positive integers greater than 0.
Find a formula for the nth term of each sequence.

-

A)
B)
C)
D)
E) None of these

Question 51

For all the problems in this set the domain is the set of positive integers greater than 0.
Find a formula for the nth term of each sequence.

-

A)
B)
C)
D)
E) None of these

Question 52

For all the problems in this set the domain is the set of positive integers greater than 0.

-Use sigma notation to represent the partial sum of the first ten terms of the sequence

A)
B)
C)
D)
E) None of these

Question 53

For all the problems in this set the domain is the set of positive integers greater than 0.

-Use sigma notation to represent the partial sum of the first eight terms of the sequence

A)
B)
C)
D)
E) None of these

Question 54

For all the problems in this set the domain is the set of positive integers greater than 0.

-Use sigma notation to represent the partial sum of the first twelve terms of the sequence

A)
B)
C)
D)
E) None of these

Question 55

For all the problems in this set the domain is the set of positive integers greater than 0.

-Evaluate the partial sum of the first four terms of the sequence

A) 12
B) 468
C) 72
D) 116
E) None of these

Question 56

For all the problems in this set the domain is the set of positive integers greater than 0.

-Evaluate the partial sum of the first four terms of the sequence

A) 44
B) 100
C) -100
D) -44
E) None of these

Question 57

For all the problems in this set the domain is the set of positive integers greater than 0.

-Evaluate the partial sum

A) 60
B) 126
C) 90
D) 100
E) None of these

Question 58

For all the problems in this set the domain is the set of positive integers greater than 0.

-Evaluate the partial sum

A) 135
B) 75
C) 150
D) 70
E) None of these

Question 59

For all the problems in this set the domain is the set of positive integers greater than 0.

-Evaluate the partial sum

A) 22
B) -22
C) 62
D) -62
E) None of these

Question 60

For all the problems in this set the domain is the set of positive integers greater than 0.

-The future value in dollars, , of an investment of $5000 that is earning 6% compounded quarterly is . Find the future value of this investment after 5 years. Round to the nearest whole number.

A) $6734
B) $6735
C) $8183
D) $8182
E) None of these