Vocab. Terms
d
common difference
5.5, 7.5, 9.5, ...
arithmetic
Given the explicit formula solve for the specified term:
an = 4(1.2)n-1
a7
a7 = 11.9
A culture of bacteria doubles every 3 hours. If there are 200 bacteria present at the
beginning, how many bacteria will there be after 24 hours?
There are 25,600 bacteria present after 24 hours.
r
common ratio
7, 5.5, 5.75,
neither arithmetic nor geometric
Determine the explicit formula of the geometric specified below:
6, 13.8, 31.74, ...
an = 6(2.3)n-1
Mrs. Readworthy is serious when she says she wants her students to study. Each week, she requires them to study 5 times the number of spelling words required the week before. If she starts off the year requiring only 1 spelling word, how many spelling words will students be studying by week 4?
Mrs. Readworthy will require 125 spelling words on week 4.
an
55, 27.5, 13.75, ...
geometric
Determine the explicit formula of the geometric specified below:
225, 45, 9, ...
an = 225(0.20)n-1
The stock's price of a company is not doing well lately. Suppose the stock's price is 92% of its previous price each day. What is the stock's price after 10 days if the stock was worth $2500 right before it started to go down?
a11 = $1085
The stock's price is about 1085 dollars.
a4
fourth term
7, 21, 63, ...
geometric
Convert the following to log form:
ax = b
logab = x
Suppose that the magnification of a PDF file on a desktop computer is increased by 15% for each level of zoom. Suppose also that the original length of the word "January" is 1.2 cm. Find the length of the word "January" after 6 magnifications.
After 6 magnifications, the length of the word "January" is 2.7756 cm.
n
index
2, 3, 5, ...
neither arithmetic nor geometric
Determine which term of the sequence is indicated by the equation below:
387,420,489 = 9(3)n
15th term
A car depreciated in value at a rate of 3% of its original price per year.
How many years does it take for the car to be worth less than $15,000 if it is originally $45,000?
37 years.