Question

Write an equation for the nth term of the geometric sequence 6. - 54, 486,

Answer 1

Given:

The geometric sequence is:

`6,-54,486,...`

To find:

The equation for the nth term of the given geometric sequence.

Solution:

We have the given geometric sequence,

`6,-54,486,...`

Here, the first term is 6 and the common ratio is:

`r=(-54)/(6)`

`r=-9`

The nth term of a geometric sequence is:

`a_n=ar^(n-1)`

Where, a is first term and r is the common ratio.

Putting
`a=6,r=-9` in the above formula, we get

`a_n=6(-9)^(n-1)`

Therefore, the equation for the nth term of the given geometric sequence is
`a_n=6(-9)^(n-1)`.