Test 2 Review

IB Math Studies
Review for Test 2
Series and Sequence
1.) Identify the following sequences as arithmetic, geometric, or neither
A.) 7, -1, -9, -17,…
B.) 7, 7, 7, 7,7,…
C.) 1, 1, 2, 3, 5, 8, …
D.) 4, -2, 1, -.5,…
2.) Given the sequence 5, 9, 13, 17, 21….
A. Find the formula for the general term.
B. Find the value of the 15th term
C. Find the sum of the first 8 terms.
3.) Given the sequence 4, -12, 36, -108,…
A. Find the formula for the general term.
B. Find the value of the 9th term.
C. Find the sum of the first 7 terms.
4.) Find k if 3k, k-2, and k + 7 are consecutive terms of an arithmetic sequence.
5.) Given the formula 𝑈𝑛 = 4𝑛 − 7
A. List the first 4 terms.
B. Prove the sequence is arithmetic using the expression 𝑈𝑛−1 − 𝑈𝑛 .
C. Evaluate ∑9𝑛=1 4𝑛 − 7
6.) * The fourth term, U4, of a geometric sequence is 135. The fifth term, U5 , is
A. ) Find the common ration of the sequence.
B.) Find U1, the first term for the sequence.
C. Calculate the sum of the first 10 terms of the sequence.
7.) Sven sells his stamp collection and deposits the proceeds of $8700 in a term
deposit account for nine month. The account pays 9.75% p.a. compounded
monthly. How much interest will he earn over this period?
8.) * In an arithmetic sequence, the filth term, U5, is greater than the first term, U1.
The difference between these terms in 36.
A.) Find the common difference, d.
The tenth term of the sequence is double the seventh term.
B.) Write down an equation in U1 and d to show this information.
C.) Find U1.
9.) Find the future value of a truck which is purchased for $135,000 and depreciates
at 15% p.a. for 5 years.
Determine the number of terms in the sequence 128, 64, 32, 16,…
and then find the sum of the series.
At the start of the dry season, Yafiah’s 3000L water tank is full. She uses
183L of water each week to water her garden.
A.) Find the amount of water left in the tank after 1, 2, 3, 4 weeks.
B.) Write a formula to describe the amount of water left in the tank in terms
of the weeks.
C.) How long does it take for the water tank to run dry?
There were originally 3000 Koala on Koala Island. Since then, the
population of koalas on the island has increased by 5% each year.
A. Write an equation represent the koala population.
B. What is the koala population after 5 years?
C. How long does it take the koala population to reach 5000?
Each year, a school manages to use 5% less paper then the year before.
If in 2000 they used 600,000 sheets of paper:
A.) How much paper did the school use in 2005?
B.) How much total paper did the school use from 2000 to 2009?
14.)* Ramon invests $18000 in a bank account that pays 3.4% nominal annual interest,
compounded quarterly. Find the minimum number of year that Ramon must invest the money
for his investment to be worth $27000.