Question

What formula can be used to find the nth term of the geometric sequence below 1/6, 1, 6, 36

Answer 1

"which formula can be used to find the nth term of the geometric system below, 
1/6, 1, 6,36"
The correct answer is D, $a_{n}$=1/6·6^n-1

Answer 2

Answer:

$a_n=a\cdot r^{n-1}\text{is the formula for used for nth term of a geometric series}$

And nth term of given geometric sequence is $a_n=36$

Step-by-step explanation:

We have been given a geometric series

$\frac{1}{6},1,6,36$

Now, we have  a formula for  $n^{th}$  term of a geometric sequence

$a_n=a\cdot r^{n-1}$

Here, $a=\frac{1}{6}$

$\text{common ratio that is r}=6$

$\text{number of terms }n=4$

On substituting the values in the formula we will get

$a_n=\frac{1}{6}\cdot 6^{4-1}$

$a_n=\frac{1}{6}\cdot 6^{3}$

$a_n=\ 6^{2}$

$a_n=36$

Therefore, nth term of given sequence is $a_n=36$