Arithmetic and Geometric Sequences

After working with patterns and attempting to organize what we see and act on it, we are formalizing our experience through a couple of weeks of analyzing arithmetic and geometric sequences both in their explicit and recursive form.  This formalization has a great deal of notation to adjust to, but is ultimately just a shorthand way of writing how the pattern works.  Can you write an explicit and recursive equations for the sequences above?

All of our homework for the next three weeks will be from It's All Connected and while I cannot upload the file here, if you are a student I can email you the file if you lose your it!

I have embedded three videos to help those of you who want to review some of the big concepts at home:

1.  Here is a video from Khan Academy on explicit and recursive definitions

Explicit and recursive definitions of sequences:

2.  Writing Recursive Formulas from Arithmetic Sequences

 

3.  Writing Recursive Formulas form Geometric Sequences

Online Practice and Videos from Khan Academy available here: https://www.khanacademy.org/math/trigonometry/seq_induction/seq_and_series/v/explicit-and-recursive-definitions-of-sequences