Question
Help please, I don't understand how to do this...
Give an example of an arithmetic sequence that is found in the real world. Find the common difference and write a recursive and iterative rule for the sequence. Use one of the rules to find another term of the sequence.
Then give an example of a geometric sequence that is found in the real world. Find the common ratio and write a recursive and iterative rule for the sequence. Use a rule to find any term.
Then clearly explain why each example is either an arithmetic or geometric sequence.
Give an example of an arithmetic sequence that is found in the real world. Find the common difference and write a recursive and iterative rule for the sequence. Use one of the rules to find another term of the sequence.
Then give an example of a geometric sequence that is found in the real world. Find the common ratio and write a recursive and iterative rule for the sequence. Use a rule to find any term.
Then clearly explain why each example is either an arithmetic or geometric sequence.
Answers
Damon
simple yearly interest rate i
(percent = 100 i)
at n = 1 first year beginning
Amount = A
second year
Amount = A + Ai
Third year
Amount = A + 2 A i
This is an arithmetic sequence with
A = starting amount
A i = d
so Amount = A + d (n-1)
recursive Amount n = Amount (n-1) + d
where d = Ai
-----------------------------
Geometric sequence = compound interest
Amount at n = (amount at n-1) * (1+i)
so
Amount at n = original amount * (1+i)^(n-1)
where n is 1 at the time of deposit
so if original amount at n = 1 is A
amount
that is of form A r^(n-1)
where r = (1+i)
and n is the number of years starting with deposit at n = 1
(percent = 100 i)
at n = 1 first year beginning
Amount = A
second year
Amount = A + Ai
Third year
Amount = A + 2 A i
This is an arithmetic sequence with
A = starting amount
A i = d
so Amount = A + d (n-1)
recursive Amount n = Amount (n-1) + d
where d = Ai
-----------------------------
Geometric sequence = compound interest
Amount at n = (amount at n-1) * (1+i)
so
Amount at n = original amount * (1+i)^(n-1)
where n is 1 at the time of deposit
so if original amount at n = 1 is A
amount
that is of form A r^(n-1)
where r = (1+i)
and n is the number of years starting with deposit at n = 1
Me and I
thank you so much!! :)
Damon
You are welcome :)
lils
was up