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 $\dfrac{5}{9}.$  

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

$a=15,~~r=\dfrac{1}{3}.$

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

$a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.$

Thus, the required fourth term in the given geometric sequence is $\dfrac{5}{9}.$