The series 2 + 4 + 8 + 16 + 32 + . . . is?

A number series is a set of numbers that follows a particular pattern throughout the series.

Answer: The 2 + 4 + 8 + 16 + 32 + . . . series is a geometric sequence or a geometric progression (G.P.’s).

Let's see the type of series given in the question.

Explanation: 

In the given series 2 + 4 + 8 + 16 + 32 + . . . , it may be seen that the ratio of two consecutive terms is the same throughout the series.

So, we will find a common ratio between successive terms and then we check whether they are equal or not.

The ratio between two consecutive terms is known as the common ratio (\(r_{n}\)).

The formula of common ratio is given as:

Common ratio, \(r_{n}\) = \(a_{n}\) / \(a_{n-1}\)

\(r_{1}\) = (second term) / (first term) = 4/2 = 2

\(r_{2}\) = (third term) / (second term) = 8/4 = 2

\(r_{3}\) = (fourth term) / (third term) = 16/8 = 2

\(r_{4}\) = (fifth term) / (fourth term) = 32/16 = 2

We can see that all four ratios come as 2.

Hence, if the given series is following this pattern, the series is known as geometric progression.

Therefore, the series 2 + 4 + 8 + 16 + 32 + . . . is a geometric sequence or a geometric progression (G.P.’s).