Question

Find the fifth term and the nth term of the geometric sequence whose initial term a1 and common ratio r are given.

Answer 1

Step 1 :

The n th term of a geometric sequence :

The n th term of a geometric sequence is .

Where is the first term and r  is the common ratio.

Step 2 :

The initial term is and common ratio is .

The n th term of a geometric sequence is

Substitute and in above equation.

The n th term of a geometric sequence is

Step 2 :

Substitute in

The fifth term of a geometric sequence is

Solution :

The n th term of a geometric sequence is

The fifth term of a geometric sequence is