Question

How do you tell whether the sequence \[2,4,8,16,32\] is arithmetic or not?

Answer 1

Hint: To solve this type we need to be clear about the definition of arithmetic series. A series is called to be arithmetic if the difference between all consecutive terms of the series is equal or same. For example: series of first $ 10 $ natural numbers, difference between each number is 1.To solve this just check the difference between consecutive terms.

Complete step-by-step answer:
Let’s try to solve this problem of checking whether the series is arithmetic or not.
Series given to check arithmetic or not is \[2,4,8,16,32\]
Now,we will apply the definition of arithmetic series to solve this that the common difference of series is the same. So let’s check
Difference between consecutive terms 2 and 4
 $ {d_1} = 4 - 2 = 2 $
Difference between consecutive terms 4 and 8
 $ {d_2} = 8 - 4 = 4 $
Difference between consecutive terms 8 and 16
 $ {d_3} = 16 - 8 = 8 $
Difference between consecutive terms 16 and 32
 $ {d_4} = 32 - 16 = 16 $
Here, we can see that this given series does not have the common difference not the same i.e., the difference between all consecutive terms of the series is equal or same.
Hence we can say that the given series \[2,4,8,16,32\] is not an arithmetic series because the given series does not have a common difference which is a necessary criteria for a series to be an arithmetic series

Note: While solving these types of questions in which you have to check whether a series is arithmetic or not. You do not have to be clear about the definition of arithmetic series. Do not end up mixing the definition of geometric series with arithmetic series.