Question

Find the missing number in the series given below: $1,2,4,8,(?),32$
a). $10$
b). $12$
c). $14$
d). $16$

Answer 1

Hint: In this question we have been given a series of number and we have to find the missing number in them. We will try to observe the given series and find the relationship between the numbers and then we can get the required answer. We should keep in mind that the series should be regular and logical.

Complete step-by-step solution:
As we know that in mathematics various problems are related to series and are based on a certain pattern which is recurring. By observing this pattern we can easily follow the series and predict the missing number.
Here we have
$1,2,4,8,(?),32$
If we observe the series carefully we can see that each of te next term gets doubled from the previous term.
As we can write the series as:
$1 \times 2 = 2$
$2 \times 2 = 4$
$4 \times 2 = 8$
So the next number will be
$8 \times 2 = 16$ .
So we can get the next number in the series i.e.
$16 \times 2 = 32$
So the missing number from the series is $16$
Hence the correct option is (d) $16$ .

Note: We should note that we can apply different types of logics to solve this kind of question. Here also we can apply the method of exponential form to solve this question.
We can write the series as
${2^0} = 1$
${2^1} = 2$
${2^2} = 4$
Now we apply the power $3$ , it gives
 ${2^3} = 8$
Similarly we have
 ${2^4} = 16$
So here we get the same answer as before.