Find the next term of a geometric sequence, given the first few terms

The  exercise appears under the Precalculus Math Mission and Integral calculus Math Mission. This exercise starts introducing the idea of basic geometric sequences.

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


 * 1) Find the next term in the sequence: This problem provides a sequence of numbers that follow a geometric progression. The student is asked to find the very next number in the sequence provided.Gs1-1.png

Strategies
Knowledge of the theory and formulas for geometric sequences and series would ensure success on this exercise.
 * 1) A geometric sequence is one in which each term is multiplied by (or divided by) a number to get successive terms.
 * 2) The ratio of a future term against it's predecessor yields the common ratio.
 * 3) The problems in this exercises always ask for the "next" term in a given sequence. This can be used to your advantage to answer the question.

Real-life Applications

 * 1) Geometric sequences model the distance travelled by bouncing objects.
 * 2) Geometric sequences and series are important to understanding Taylor and Maclaurin series approximations of general functions.
 * 3) Many puzzles and challenge problems use geometric sequences because the results can often be surprising or non-intuitive.