Answer:
The explicit form is [tex]a_{n}=162(2/3)^{n-1}[/tex]
Step-by-step explanation:
The explicit form of a geometric sequence is given by:
[tex]a_{n}=ar^{n-1}[/tex]
where an is the nth term, a is the first term of the sequence and r is the common ratio.
In this case:
a=162
The value of the common ratio is obtained by dividing one term by the previous term.
For the first and second terms:
108/162=2/3
For the second and third terms (In order to prove that 2/3 is the common ratio)
72/108=2/3
Therefore:
r=2/3
Replacing a and r in the formula:
[tex]a_{n}=162(2/3)^{n-1}[/tex]
