Geometric Sequences Lesson

A Geometric Sequence, is a set of terms in which each term after the first is obtained by multiplying the preceding term by the same fixed number called the Common Ratio which is commonly represented by r.

The number pattern 1, 2, 4, 8, 16,… is a geometric sequence. Two is

multiplied to any term to get the next term. Therefore, we can say that 2 is the common ratio. The common ratio may be an integer or fraction, negative or positive. It can be found by dividing any term by the term that precedes it.

Since the common ratio is 2 and the first term is 1,

In the sequence 3, 8, 13, 18, 23 …there is no common ratio among the terms. However, there is a common difference of 5. To prove, let us have the following solution: