Question

What is the value of the fourth term in a geometric sequence for which a1=15 and r=1/3

express your answer as a fraction

Answer 1

nth term = a1r^(n-1)

4th term = 15* (1/3)^3 = 15/27 = 5/9

Answer 2

Answer: The required fourth term in the given geometric sequence is
`(5)/(9).`

Step-by-step explanation: We are given to find the fourth term of a geometric sequence with the following first term and common ratio :

`a=15,~~r=(1)/(3).`

We know that

the nth term of a geometric sequence with first term a and common ratio r is given by

`a_n=ar^(n-1).`

Therefore, the forth term of the given geometric sequence is

`a_4=ar^(4-1)=ar^3=15*\left((1)/(3)\right)^3=15*(1)/(27)=(5)/(9).`

Thus, the required fourth term in the given geometric sequence is
`(5)/(9).`