Geometric Sequences Lesson

Q1W3 Geometric Sequences Lesson

by: Nickson T. Derraco

Mathematics Teacher

Geometric Sequence

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.

Illustrative Example 1

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.

Using the picture above, we illustrated and proved that the common ratio

is equal to 2.

Now, let us determine the next two terms in the given sequence 1, 2, 4, 8,

16,…

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

Thus, the next two terms of the geometric sequence 1, 2, 4, 8, 16, are 32 and 64.

What do you think are the 8th and 9th terms of this sequence? 

Illustrative Example 2.

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:

Thus, this is not a geometric sequence but an arithmetic sequence.