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

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.