Deck 12: Sequences and Series

Question 1

Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference.

Answer 1

It is arithmetic, the common difference is .

Question 2

Find the first four terms and the term of the sequence .

Answer 2

, , , , .

Question 3

Find the first four partial sums and the partial sum of the sequence .

Answer 3

Question 4

Find the term of the sequence whose first several terms are , , , , .

Question 5

A fish farmer has 5000 catfish in his pond. The number of catfish increases by 8% per month, and the farmer harvests 200 catfish per month. The catfish population after n months is given recursively by and . How many fish are in the pond after 6 months?

Question 6

Write the sum using sigma notation.

Question 7

Write the sum without using sigma notation.

Question 8

Find the term of the sequence whose first several terms are , , , , .

Question 9

Find the term of the sequence whose first several terms are , , , , .

Question 10

Find the first six partial sums , , , , , and of the sequence . .

Question 11

Find the term of the sequence .

Question 12

Find the first five terms of the sequence , which is defined recursively.

Question 13

A fish farmer has 5000 catfish in his pond. The number of catfish increases by 8% per month, and the farmer harvests 200 catfish per month. The catfish population after n months is given recursively by and . How many fish are in the pond after 5 months?

Question 14

Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference.

Question 15

A city was incorporated in 2004 with a population of 45,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence
(a) Find the first 5 terms of the sequence.
(b) Find the population in 2014.

Question 16

Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference.

Question 17

Find the first four terms and the term of the sequence .

Question 18

Find the first four terms and the term of the sequence .

Question 19

A city was incorporated in 2004 with a population of 25,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence
(a) Find the first 5 terms of the sequence.
(b) Find the population in 2014.

Question 20

Find the first four terms and the term of the sequence .

Question 21

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 22

Which term of the arithmetic sequence is ?

Question 23

Find the sum of the first 50 even integers.

Question 24

Given the partial sum of an arithmetic sequence . Find its sum.

Question 25

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 26

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 27

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 28

A man gets a job with a salary of $40,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period.

Question 29

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 30

The seventh term of an arithmetic sequence is and the seventeenth term is . Find the twenty-fourth term.

Question 31

Determine whether the sequence is geometric. If it is geometric, find the common ratio.

Question 32

An arithmetic sequence has first term and common difference . How many terms of this sequence must be added to get

Question 33

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period.

Question 34

Given that the term of an arithmetic sequence is and the common difference is , find the first three terms.

Question 35

A large outdoor amphitheater has rows of seats with seats in the first row, seats in the second, in the third, and so on. How many seats are in row How many seats are there in the theater? How many seats total are there in rows through

Question 36

Find the term of the arithmetic sequence given and .

Question 37

The first term of the arithmetic sequence is and the common difference is . Which term of this sequence is ?

Question 38

Given that the term of an arithmetic sequence is and the term is , find the first term.

Question 39

Determine the common difference, the fifth, , and terms of the arithmetic sequence .

Question 40

Determine whether the sequence is geometric. If it is geometric, find the common ratio.

Question 41

A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from ft above the ground, until it comes to rest.

Question 42

Express the repeating decimal as a fraction.

Question 43

Determine the common ratio, the fifth, and the terms of the geometric sequence

Question 44

A culture initially has 7000 bacteria, and its size increases by 8% every hour. How many bacteria are present at the end of 5 hours? Find a formula for the number of bacteria present after n hours.

Question 45

Find the first five terms, the common ratio, and the term expressed in standard form of the geometric sequence .

Question 46

Determine the common ratio, the fifth, and the terms of the geometric sequence .

Question 47

Determine whether the sequence is geometric. If it is geometric, find the common ratio.

Question 48

Determine the common ratio, the fifth, and the terms of the geometric sequence.

Question 49

Find the fourth term and the term of the geometric sequence given and .

Question 50

Determine the common ratio, the fifth, and the terms of the geometric sequence

Question 51

Which term of the geometric sequence is ?

Question 52

Find the sum .

Question 53

Find the sum of the infinite geometric series .

Question 54

The first term of a geometric sequence is and the second term is . Find the fifth term.

Question 55

Find the partial sum of the geometric sequence with , .

Question 56

Find the first five terms, the common ratio, and the term expressed in standard form of the geometric sequence .

Question 57

Find the partial sum of the geometric sequence with , .

Question 58

A culture initially has 6000 bacteria, and its size increases by 8% every hour. How many bacteria are present at the end of 5 hours? Find a formula for the number of bacteria present after n hours.

Question 59

Express the repeating decimal as a fraction.

Question 60

Find the sum of the infinite geometric series .

Question 61

How much must be invested now at 6.5% per year compounded quarterly, to fund an annuity of 15 quarterly payments of $500 each, the first payment being three months after the initial investment?

Question 62

A farmer wants to borrow $50,000 in order to buy a tractor. She wants to repay the loan by semi-annual installments for six years. If the interest rate is 10% per year compounded semi-annually, what is the amount of each payment?

Question 63

How much money must be invested now at 16% per year compounded quarterly, to fund an annuity of quarterly payments of each, the first payment being three months after the initial investment?

Question 64

What is the monthly payment on a 20 year mortgage of $85,000 at 9% interest per year, compounded monthly? What is the total amount paid on this loan over the 20 year period?

Question 65

A couple can afford to pay $825 per month toward buying a house. If the mortgage rate is 6.25% and they intend to secure a 15year mortgage, how much can they borrow? How much can they borrow if they intend on securing a 30 year mortgage?

Question 66

Find the amount of an annuity that consists of 8 monthly payments of $1200 each into an account that pays interest per year.

Question 67

Kristi decides to buy a new car for $25,000 and make payments of $525 per month for 6 years. What interest rate is she paying on the loan?

Question 68

Use mathematical induction to prove that the formula is true for all natural numbers .

Question 69

Find the amount of an annuity that consists of 15 annual payments of $200 each into an account that pays interest per year.

Question 70

Find the amount of an annuity that consists of 52 weekly payments of $10 each into an account that pays 3% interest per year.

Question 71

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

Question 72

How much money should be invested monthly at 6% per year, compounded monthly, in order to have in two years?

Question 73

What is the monthly payment on a 50 year mortgage of $500,000 at 12% interest per year, compounded monthly? What is the total amount paid on this loan over the 50 year period?

Question 74

Mike buys a stereo by paying $50 a month for two years. If the interest rate is 12% per year, compounded monthly, what is the price of the stereo?

Question 75

Find the amount of an annuity that consists of 30 annual payments of $500 each into an account that pays interest per year.

Question 76

Use mathematical induction to prove that the sum of a partial geometric sequence is .

Question 77

How much money should be invested monthly at 18% per year, compounded monthly, in order to have in ten months?

Question 78

How much money must be invested now at 5% per year compounded semi-annually, to fund an annuity of semi-annual payments of each, the first payment being six months after the initial investment?

Question 79

Alyson buys a computer by paying $15 a week for three years. If the interest rate is 10.4% per year, compounded weekly, what is the price of the computer?

Question 80

Dr. Stevens is considering a 30-year mortgage at 6% interest. She can make payments of $2500 a month. What size loan can she afford?