Question

Find the common ratio and an explicit form in each of the following geometric sequences.

Answer 1

Answer:

The explicit form is $a_{n}=162(2/3)^{n-1}$

Step-by-step explanation:

The explicit form of a geometric sequence is given by:

$a_{n}=ar^{n-1}$

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:

$a_{n}=162(2/3)^{n-1}$