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:

$r=\dfrac{-54}{6}$

$r=-9$

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 $a_n=6(-9)^{n-1}$.