Question

Need help geometric sequences see pic for details

Answer 1

Given:

The recursive formula of a geometric sequence is

$a_n=a_{n-1}\cdot (\dfrac{1}{8})$

$a_1=-3$

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is $a_1=-3$.

Recursive formula of a geometric sequence is

$a_n=a_{n-1}\times r$      ...(i)

where, r is common ratio.

We have,

$a_n=a_{n-1}\cdot (\dfrac{1}{8})$    ...(ii)

On comparing (i) and (ii), we get

$r=\dfrac{1}{8}$

The explicit formula of a geometric sequence is

$a_n=a_1r^{n-1}$

Putting $a_1=-3$ and $r=\dfrac{1}{8}$, we get

$a_n=-3\left(\dfrac{1}{8}\right)^{n-1}$

Therefore, the correct option is D.