Geometric Sequences
1) A geometric sequence has the form 6, 2, 2/3…
a. State the common ratio.
b. Calculate the 10th term of the sequence.
2) A geometric sequence has all positive terms. The first term is 5 and the third term
is 20.
a. Find the common ratio.
b. Find the 7th term in the sequence.
3) Consider the geometric sequence -16, a, -4, …
a. Find the value of a
b. Find the value of the eight term.
4) A geometric sequence has a second term of 21 and a fourth term of 5.25.
a. Find the common ratio.
b. Find the sum of the first 10 terms.
5) The first 3 terms of a geometric sequence are -2, 6, -18…
a) State the common ratio for this sequence
b. Calculate the sum of the first 12 terms of the sequence.
6) Find the sum of the geometric sequence 2, 4, 8, 16,… 8192
7) A plant is .8m tall. It grows 2% each week. Find how tall it will be after 10 weeks.
8) A car is worth 75000 GBP. Each year it looses 8 percent of its value. How much is
the car worth after 5 years?
9) A mysterious illness is affecting the residents of Gezonddorp. The first day 8
people are sick. The second day 24 new people have the illness, and the third 72
new people have the illness.
a) Show that the number of ill people forms a geometric sequence.
b) Find out how many new people have the illness on the 5th day.
c) Find the total number of people that have the illness in the first
week.
10) On her 21st birthday Isabel received 80 Jordanian Dinar for allowance the first
month after her birthday and a 5% increase every month after that.
a. Find how much her allowance is after 8 months.
b. Calculate the total amount of money she received during the first
year.
Currency exchange
1) Jasmin is traveling from Rotterdam to Los Angeles. She changes 2500 euros to US
dollars at an exchange rate of 1 EUR to 1.319 USD. Give all answers correct to 2
decimal places.
a. How many USD does Jasmin receive?
Jasmin spend 2050 USD and then decides to convert the remaining money back to
euros at a rate of 1 EUR to 1.328 USD.
b. What is the amount of euros that she receives?
If she had waited to change her money back until she got to Rotterdam she could
have changed it at a rate of 1 EUR to 1.261 USD but the bank would have charged
.6% commission.
c. Caculate the amount of money that Jasmin either gained or lost by
exchanging her money in Los Angeles.
2) Currency conversion table
EUR
USD
JPY
GBP
Euros (EUR)
1
p
q
.852
US Dollar (USD)
.759
1
81.92
.647
Japanese Yen (JPY)
.00926
.0122
1
.0079
British Pounds (GBP) 1.174
1.546
126.65
1
From the table 1USD=0.647 GBP
a. Find the values of p and q
b. Muriel wants to change money at a bank in Bristol
i. How many euros did she exchange if she received 150 GBP?
ii. The bank charges a 2.4% commission on all transactions. If
she makes this transaction, how many GBP will she actually
receive?
3) Minni visits Britain from America and exchanges 3000 USD into GBP at a rate of
1 USD= 0.652 GBP. The bank charges 2.5% commission.
a. How many GBP does she receive?
After Britain, Minni travels to Italy. She changes 550 GBP to euros at an exchange
rate of 1GBP= 1.8 euros. The bank charges commission and gives Minni 629 euros.
b. Find the commission in GBP.
Chapter 1 Review
1) Come up with an acronym for conversions (use the first letter (or 2 for deca) to
create one)
kg hm dam m dm cm mm
2) What is the best unit to use when measuring
a. A person’s height?
b. The length of a football field?
d. Distance from New York City to Washington D.C?
e. The width of a book?
f. The diameter of a screw?
g. The length of a car?
3) Convert the following
a. 5m to cm
b. 16.3 hm to m
c. .37 hm to m
d. 71 dm to km
e. .023 mm to m
f. .00037 km to cm
4) Convert the following
a. 5m2 to cm
b. 16.3 hm3 to m3
c. .37 hm3 to m3
d. 71 dm2 to km2
e. .023 mm2 to m2
f. .00037 km3 to cm3
5) Estimate
a. The area of a piece of paper that is 30cm by 18cm
b. The weight of 1 piece of chocolate if the whole bag of 22 pieces weighs
2014 g.
c. People can sit in an auditorium that has 14 rows of 12 seats
d. How much time is spent watching season one of HIMYM (22 episodes 21
minutes an episode, no commercials)
6) Calculate your percent error for all parts of the last problem.
7)
Number
ℕ
ℚ
ℝ
ℤ
-6/7
√9
√47
−2𝜋
-40/10