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.

4 answers

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

thank you so much!! :)

You are welcome :)

was up