Download Geometric Sequence WS - Algebra with Mrs. Jett!

Acc Alg I/Geo A
Geometric Sequences
Name _____________________________
Problem: Your room is too cold so you decide to adjust the thermostat. The current temperature of the
room is 60o Fahrenheit. In an attempt to get warmer, you increase the temperature by 10% every hour.
An hour later, it’s still not warm enough, so you increase it by 10% again. When this still isn’t effective,
you continuously increase the temperature in this manner.
Write the sequence of temperatures (round to the nearest degree): ____________________________________
_
Can you write a formula to generate this sequence?
Geometric Sequence:
A sequence of numbers in which the ratio between any two
consecutive terms is a constant. In other words, it is a sequence of numbers in which you multiply each
term by a constant to determine the next term.
This constant is called the common ratio, represented by the letter r.
Explicit Formula:
Recursive Formula:
Formulas for our example:
What is the temperature in the room if we adjust it 12 times? _________________________________________
Example: Write the recursive and explicit formula for each of the following sequences. Then identify the
next 3 terms and the 10th term.
1) 1, 3, 9, 27, 81…
2) 1, -2, 4, -8, 16…
1 1
3) 4, 2, 1, 2, 4,…
2
4) 𝑎1 = 3 , 𝑟 = 6
Example: Animals plants, fungi, slime, molds, and other living creatures consist of eukaryotic cells.
During growth, generally there is a cell called “mother cell” that divides itself into two “daughter cells.”
Each of those daughter cells then divides into two more daughter cells, and so on. The sequence to
represent the growth is:
1, 2, 4, 8, 16…
Write the explicit formula:
Write the recursive formula:
How many cells will there be after the 10th cell division?
Example: A mine worker discovers an ore sample containing 500 mg of radioactive material. It is
discovered that the radioactive material has a half-life of 1 day. Write the explicit formula for this
situation, graph the situation, and find the amount of radioactive material in the sample at the beginning
of the 7th day.
Acc Alg I/Geo A
Geometric Sequences Worksheet
Name ____________________________
Determine whether the following sequences are arithmetic, geometric, or other. If arithmetic or
geometric, identify the common difference or common ratio, write the explicit and recursive formula, and
find the 10th term.
1)
5
, 5, 15, 45,…
3
4) -3, 1, 5, 9,…
2) 1, 4, 9, 16,…
3) -45, -61, -77, -93,…
5) -30, 15, -7.5, 3.75,…
For each geometric sequence, write the recursive and explicit formulas. Then find the 8th term.
6)
7)
8)
9)
Write an explicit formula for the following situations and use it to answer the questions.
10) The end of a spring is pulled as far as it will go and then is released. On the first bounce back it
extends 54 cm. On its second bounce back it extends 18 cm. On its third bounce back it extends 6 cm. How
long does the spring extend after 7, 8, 9, and 10 bounce backs?
11) Gordon Moore, co-founder of Intel, suggested that the number of transistors on a square inch of
integrated circuit in a computer chip would double every 18 months. If the number of transistors on a
square inch of integrated circuit started at 10, find the number of transistors over the course of the next
10 years.
12) A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many
bacteria will there be after 24 hours? Graph this situation.