Question

Identify the following series as arithmetic, geometric, both, or neither. -3 + 3 - 3 + 3 - 3 + . . .

Answer 1

Arithmetic would be the answer to the question

Answer 2

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

$3-(-3)=6,~~~-3-3=6,~~~3-(-3)=6,~.~.~.$

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

$\dfrac{3}{-3}=\dfrac{-3}{3}=~.~.~.=-1.$

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.