Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

Answer 1

Given:

The geometric sequence is:

$n$              $a_n$

1                        -4

2                      20

3                     -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

$a_n=ar^{n-1}$            ...(i)

Where, a is the first term, r is the common ratio and $n\geq 1$.

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{20}{-4}$

$r=-5$

Putting $a=-4,r=-5$ in (i), we get

$a_n=-4(-5)^{n-1}$ where $n\geq 1$

Therefore, the correct option is B.