What is the common ratio between successive terms in the sequence? 27, 9, 3, 1,…
Solution:
Given: Sequence is 27, 9, 3, 1,…
A sequence in which the ratio between two consecutive terms is the same is called a geometric sequence.
A geometric progression is a sequence where every term bears a constant ratio to its preceding term.
The geometric sequence is generally represented in form a, ar, ar2, ... where a is the first term and r is the common ratio of the sequence.
The ccommon ratio can have both negative as well as positive values.
The common ratio of a geometric progression is calculated by dividing two consecutive terms and simplifying it to the simplest form.
a\(_2\)/a\(_1\) = 9/27 = 1/3
a\(_3\)/a\(_2\) = 3/9 = 1/3
a\(_4\)/a\(_3\) = 1/3
In the sequence, the ratio 1/3 is the same and is called the common ratio.
Therefore, the common ratio for the given sequence is 1/3.
What is the common ratio between successive terms in the sequence? 27, 9, 3, 1,…
Summary:
The common ratio between successive terms in the sequence 27, 9, 3, 1,... is 1/3.
visual curriculum