# 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 in geometric sequences or geometric progressions (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 progressions.