Find recursive formulas for geometric sequences

The  exercise appears under the Algebra I Math Mission and Precalculus Math Mission. This exercise increases familiarity with the recursive formula for geometric sequences and it's relation to the explicit formula.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the explicit formula: This problem provides a geometric sequence written in the recursive form. The student is expected to find the explicit form and write it in the space.Rffgs1.png
 * 2) Determine the appropriate parameters: This problem gives a geometric sequence in some form, such as a table or a rule. The student is expected to find the values of the parameters to correctly express the recursive form of the sequence.Rffgs2.png

Strategies
Knowledge of the geometric sequence and series formulas are encouraged to ensure success on this exercise.
 * 1) The nth term of an arithmetic sequence is given by $$g_n=g_1r^{n-1}$$.
 * 2) The formula does not need to be distributed or simplified on this exercise to be considered correct.
 * 3) The first parameter in the recursive form is the first term, and the missing parameter in the second part is the common ratio between successive terms.

Real-life Applications

 * 1) Sequences and series are common problem on IQ tests.
 * 2) Sequences and series are a large portion of second semester (BC) calculus.
 * 3) An ability to abstract from observations is a skill that mathematicians need in upper-division mathematics (inductive reasoning vs. deductive reasoning).