Deck 10: Binomial Expansions, Sequences, and Series

Question 1

Find a formula for the nth term of the sequence.

Answer 1

A

Question 2

Evaluate the expression.

A) 6
B) 20
C) 23
D) 1

Answer 2

B

Question 3

How many terms are in the expansion of ?

A) 15
B) 17
C) 14
D) 16

Answer 3

D

Question 4

List the terms of the sequence.

Question 5

List the terms of the sequence.

Question 6

List the terms of the sequence.

Question 7

Find a formula for the nth term of the sequence.

Question 8

Find the indicated term of the binomial expansion.

Question 9

Use the binomial theorem to expand the binomial.

Question 10

Find a formula for the nth term of the sequence.

Question 11

Question 12

Expand the binomial. Use Pascal's triangle to find the coefficients.

Question 13

Question 14

Find the first three terms of the expansion.

Question 15

Question 16

List the terms of the sequence.

Question 17

Find a formula for the nth term of the sequence.

Question 18

Expand the binomial. Use Pascal's triangle to find the coefficients.

Question 19

Use the binomial theorem to expand the binomial.

Question 20

A) 2
B) 1
C) 20
D) 114

Question 21

Find the sum.

A) 65
B) 175
C) 195
D) 45

Question 22

Find the sum.

A) -12
B) 12
C) -84
D) 84

Question 23

Write the nth term of the arithmetic sequence. 0, 3, 6, 9, 12

Question 24

Write the series in summation notation.

Question 25

Cameron deposited $650 in an account that pays 4% interest compounded annually. Write a sequence representing the amount Cameron receives in interest each year for the next 4 years.
Round each term to the nearest cent.

A) $26.00, $52.00, $78.00, 104.00
B) $26.00, $52.00, $104.00, $208.00
C) $26.00, $27.04, $28.12, $29.25
D) $26.00, $27.04, $27.46, $27.62

Question 26

Write the first five terms of the arithmetic sequence.

Question 27

Find the twelfth term of the arithmetic sequence given

A) 88
B) 51
C) 55
D) 81

Question 28

Find the common difference d for the arithmetic sequence. 4, -5, -14, -23, -32, ...

A) -4
B) 4
C) 9
D) -9

Question 29

Find the sum.

Question 30

Write the series in summation notation.

Question 31

Write the series in summation notation.

Question 32

Write the series in summation notation.

Question 33

Find the sum.

A) 75
B) 150
C) 110
D) 220

Question 34

List the first five terms of the sequence.

Question 35

Find the sum.

A) 6
B) 10
C) 12
D) 8

Question 36

Find the seventh term of the arithmetic sequence given

A) -54
B) -44
C) -50
D) -62

Question 37

Write the first five terms of the arithmetic sequence.

Question 38

Find the common difference d for the arithmetic sequence. -4, 4, 12, 20, 28, ...

A) 8
B) 4
C) -8
D) -4

Question 39

Write the nth term of the arithmetic sequence.

Question 40

Write the nth term of the arithmetic sequence. 3, -2, -7, -12, -17, ...

Question 41

Determine the common ratio, r, for the geometric sequence.

Question 42

A home purchased for $105,000 increases by 3% of its value each year. The value of the home after n years is given by Find the value of the home after 5 years by computing . Round to the nearest dollar.

Question 43

Find the nth term of the geometric sequence.

Question 44

A ball drops from a height of 6 ft. With each bounce, the ball rebounds to of its height. The total vertical distanced traveled is given by After the first term, the series is an infinite geometric series. Compute the total vertical distance traveled.

A) The total vertical distance traveled is 10 ft.
B) The total vertical distance traveled is 14 ft.
C) The total vertical distance traveled is 4 ft.
D) The total vertical distance traveled is 8 ft.

Question 45

The seating in a certain theater is arranged so that there are 44 seats in row 1, 45 seats in row 2, 46 seats in row 3, and so on. If there are 25 rows, what is the total revenue is the average ticket price is
$8)00 per seat and the theater is sold out?

A) $11,200.00
B) $272.00
C) $6800.00
D) $448.00

Question 46

Find the indicated term of the geometric sequence.

Question 47

Find the sum of the geometric series. 7 + (-14) + 28 + (-56) + 112

A) 21
B) -147
C) -35
D) 77

Question 48

Determine the sum of the infinite series, if it exists.

Question 49

Find the sum of the geometric series.

Question 50

Find the number of terms, n, of the arithmetic sequence. -1, -9, -17, ..., -217

A) 30
B) 28
C) 27
D) 29

Question 51

Find the nth term of the geometric sequence. -8, 16, -32, 64, ...

Question 52

Find the sum of the arithmetic series.

A) 154
B) 88
C) 175
D) 155

Question 53

Find the sum of the arithmetic series.

Question 54

Determine the sum of the infinite series, if it exists.

Question 55

Find the sum of the first 20 positive multiples of 4.

A) 840
B) 800
C) 36
D) 40

Question 56

Find the sum of the arithmetic series. -1 + (-6) + (-11) + ... + (-46)

A) -210
B) -235
C) -230
D) -205

Question 57

Determine the common ratio, r, for the geometric sequence. -6, 24, -96, 384, ...

A) -30
B) 4
C) 30
D) -4

Question 58

Write the first five terms of the geometric sequence. a1 = -6, r = -1

A) -1, -7, -13, -19, 11
B) -6, 6, -6, 6, -6
C) -1, 6, -36, 216, -1296
D) -6, -7, -8, 9, -10

Question 59

Find the number of terms, n, of the arithmetic sequence.

Question 60

Find the indicated term of the geometric sequence.