Module 7, Recursively-Defined Sequences & Iterations Assignment
You have learned how to write both the explicit and recursive forms of arithmetic and geometric
sequences. You can solve for a term directly using the explicit form. In a recursive form, you
need to know the value of all the terms that come before the term you are looking for. For
example, to find the value of the 10th term in a recursively-defined sequence, you need to know
the values of term 1 to term 9. Finding the values of terms in recursively-defined sequences is
similar to the process of iteration. Both recursively-defined sequences and iteration use their own
notation.
Consider the scenario below.
This morning Haidar noticed that her dog, Aldi,
seemed unwell. She took him to the vet, where he
was diagnosed with an ear infection. The
veterinarian prescribed an antibiotic called
amoxicillin to help Aldi feel better. Haidar will
give Aldi 150 mg of the antibiotic once each day
for 10 days. Each time Haidar gives Aldi his next
dose of medication, 40% of the previous dose
remains in his bloodstream.
Use what you know about recursive sequences and iteration to explore the mathematics related to
this scenario.
1. Determine the amount of medication that is in Aldi’s bloodstream after Haidar gives him each
of the 1st, 2nd, 3rd, and 4th doses of amoxicillin. Show your work.
2. Use your response to question 1 to write a recursive definition for the amount of medication in
Aldi’s bloodstream after each dose of medication. Is your definition arithmetic, geometric, or
neither? Explain.
1st 150
2nd 150+60=210
3rd 150+84= 234
4th 150+93.6= 243.6
an=150+(0.4*an-1)
a1=150
This is really neither because there is no common difference or common ratio
