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.
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 (rn).
The formula of common ratio is given as:
Common ratio, rn = an / an−1
r1 = (second term) / (first term) = 4/2 = 2
r2 = (third term) / (second term) = 8/4 = 2
r3 = (fourth term) / (third term) = 16/8 = 2
r4 = (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.