Finite geometric series word problems

The  exercise appears under the Precalculus Math Mission. This exercise applies the geometric series formula to word problems.

Types of Problems
There is one type of problem in this exercise:


 * 1) Answer the problem in context: This problem provides a context driven word problem involving a geometric sequence. The student is asked to find the appropriate sum to answer the question and write it in the space provided.Fgswp1.png

Strategies
Knowledge of formulas and patterns from geometric sequences and series are encouraged to ensure success on this exercise.
 * 1) The finite geometric sum formula is $$ S_n=\frac{g_1(1-r^n)}{1-r}$$.
 * 2) The answers in these problems will be positive, so a negative result indicates an error in calculation.

Real-life Applications

 * 1) Sequences are series are fundamental to the calculus, which has many applications to real life.
 * 2) Sequences are common on IQ tests for measuring pattern recognition ability.
 * 3) Taylor Series can be used to approximate complicated functions via polynomials.
 * 4) Some of the problems in this exercise involve fractals (like the Sierpinski gasket) and physics (like distance travelled by bouncing balls).
 * 5) The problems in this exercise are applications.