Question

One term of a geometric sequence is a4=135. The common ratio is r=3. Write an explicit rule for the nth term.

Answer 1

Answer:

$a_{n} = 5 * 3^{n-1}$

Step-by-step explanation:

To find the nth term of a geometric sequence, you have the general formula:

$a_{1} *r^{n-1}$

where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):

135 = $a_{1} * 3^{4 - 1}$

135 = $a_{1} * 3^3$

135 = $27a_{1}$

$a_{1} = 5$

Now, we can substitute the first term back in:

$a_{n} = 5 * 3^{n-1}$