The explicit formula for the geometric sequence with this recursive
formula will be; [tex]a_n=-3(1/8)^{n-1}[/tex]Therefore, the option D is the correct.
What is a geometric sequence and how to find its nth terms?
Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
a, ar, ar^2, ar^3, \cdots
(till the terms to which it is defined)
Thus, the nth term of such sequence would be T_n = ar^{n-1} (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
The sum of terms of a geometric sequence;
Lets suppose its initial term is a, multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We have been given;
[tex]a_1 = -3\\a_n= a_{n-1} (1/8)[/tex]
So, the explicit formula for the geometric sequence with this recursive
formula will be;
[tex]a_n=-3(1/8)^{n-1}[/tex]
Therefore, the option D is the correct.
Learn more about geometric sequence here:
https://brainly.com/question/2735005
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