Question

How to find the common ratio of a geometric sequence?

Answer 1

To find the common ratio of a geometric sequence, divide any term (except the first) by the preceding term, and simplify if necessary. This ratio will be consistent across all consecutive pairs of terms in a geometric sequence.

Step-by-step explanation:

Finding the Common Ratio in a Geometric Sequence

To find the common ratio of a geometric sequence, you must take any term in the sequence (after the first) and divide it by the term directly preceding it. This ratio should remain constant throughout the sequence. For example, if the sequence is 2, 4, 8, 16, ..., then the common ratio (r) can be found by dividing the second term by the first term:

r = 4 / 2 = 2

Or the third term by the second term:

r = 8 / 4 = 2

And so on. This confirms that the common ratio is indeed 2. Remember, if the sequence is correctly identified as geometric, the ratio will be the same no matter which two consecutive terms are used to calculate it.

Simplifying fractions as needed, ensures that the ratio is in its simplest form. In this case, 2 : 2 simplifies to 1 : 1.

Answer 2

if the sequence is say,
a,b,c,d ,....
then the common ratio r can be found by

r = b/a
or
r = c/b
or
r= d/c
and so on.