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

`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`

Explanation:

We have been given a geometric series

`(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=(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=(1)/(6)\cdot 6^(4-1)`

`a_n=(1)/(6)\cdot 6^(3)`

`a_n=\ 6^(2)`

`a_n=36`

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