Answer: The correct option is (D) geometric.
Step-by-step explanation: We are given to identify the type of the following series as arithmetic, geometric, both or neither:
-3 + 3 - 3 + 3 - 3 + . . . .
We can see that the first term of the series is - 3.
(A) To be an arithmetic series, each term differs from its preceding term by the same quantity.
But, here we notice that
[tex]3-(-3)=6,~~~-3-3=6,~~~3-(-3)=6,~.~.~.[/tex]
So, the difference is not same and hence the given series cannot be arithmetic.
(B) To be a geometric series, the ratio of any term to its preceding same must be same.
We notice that
[tex]\dfrac{3}{-3}=\dfrac{-3}{3}=~.~.~.=-1.[/tex]
So, the given series is a geometric one with fert term -3 and common ratio -1.
Thus, the given series is geometric.
Option (D) is CORRECT.
We can see that this is a geometric series with a common ratio of -1.
A geometric sequence is a sequence where each term is given by the product between the previous term and a constant ratio.
In this case, the first element is -3.
To get the next term, 3, we need to multiply the previous one by -1.
-3*-1 = 3
To get the next term, -3, we can multiply by -1 again:
3*(-1) = -3
And so on.
So we can see that this is a geometric series with a common ratio of -1.
if you want to learn more about geometric sequences:
https://brainly.com/question/1509142
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