Solving application problems with geometric sequences
In real-world scenarios involving arithmetic sequences, we may need to use an initial term of
instead of
In these problems, we can alter the explicit formula slightly by using the following formula:
Solving application problems with geometric sequences
In 2013, the number of students in a small school is 284. It is estimated that the student population will increase by 4% each year.
Write a formula for the student population.
Estimate the student population in 2020.
The situation can be modeled by a geometric sequence with an initial term of 284. The student population will be 104% of the prior year, so the common ratio is 1.04.
Let
be the student population and
be the number of years after 2013. Using the explicit formula for a geometric sequence we get
We can find the number of years since 2013 by subtracting.
We are looking for the population after 7 years. We can substitute 7 for
to estimate the population in 2020.
A business starts a new website. Initially the number of hits is 293 due to the curiosity factor. The business estimates the number of hits will increase by 2.6% per week.
recursive formula for
term of a geometric sequence
explicit formula for
term of a geometric sequence
Key concepts
A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant.
The constant ratio between two consecutive terms is called the common ratio.
The common ratio can be found by dividing any term in the sequence by the previous term. See
[link] .
The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. See
[link] and
[link] .
A recursive formula for a geometric sequence with common ratio
is given by
for
.
As with any recursive formula, the initial term of the sequence must be given. See
[link] .
An explicit formula for a geometric sequence with common ratio
is given by
See
[link] .
In application problems, we sometimes alter the explicit formula slightly to
See
[link] .
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
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Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.