Question

How is the common ratio of a geometric sequence found?

Answer 1

Geometric sequence:

A geometric sequence is a sequence in which any term divided by its previous term is a constant. That is, each term of a geometric sequence is obtained by multiplying a constant number to its previous term.

 

This constant is known as the common ratio of the geometric sequence and it is denoted by ‘r.’

If a1 is the first term of a geometric sequence and r is its common ratio, then the sequence will be,

{a1, a1 × r, a1 × r2, a1 × r3, …}

 

If it is known that a sequence is a geometric sequence, its common ratio can be found in the following manner:

1. Choose any term in the given geometric sequence.

2. Divide the chosen term by its previous term.

3. The quotient obtained will be the common ratio of the given geometric sequence.

 

For example:

The sequence {54, 18, 6, 2, 2/3, …} is a geometric sequence.

Compute the common ratio of the above sequence. Divide any term from its previous term.

 

Chose any term (consider term third),

Divide third term by second term,

a3 ÷ a2 = 6 ÷ 18

              = 1/3

 

The quotient obtained is equal to 1/3, the common ratio of the given geometric sequence will be r = 1/3.

The quotient obtained is equal to 1/3, the common ratio of the given geometric sequence will be r = 1/3.