Question

Which number will complete the given series?
 \[2,4,6,8,\] ?
A. \[10\]
B. \[11\]
C. \[12\]
D. \[13\]

Answer 1

Hint: A series is nothing but numbers arranged in a particular order. For instance, in a series the difference between each consecutive two numbers can be equal or a series can contain a multiple of any number. So that we have to first find the difference between the consecutive pair of numbers so that we can find the relation between the numbers in that series.

Complete step by step answer:
The series given is \[2,4,6,8,?\] . Our aim is to find the next number in the series. We first try to find the relationship between these numbers in the series. Let us find the difference between the consecutive pairs.
The first consecutive pair is \[2,4\] . Difference between them is ( \[4 - 2 = 2\] ) two.
The next consecutive pair is \[4,6\] . Difference between them is ( \[6 - 4 = 2\] ) two.
The next consecutive pair is \[6,8\] . Difference between them is ( \[8 - 6 = 2\] ) two.
Thus, we can see that the difference between each consecutive number is two. Then the difference between the next number and \[8\] has to be two.
Now let us find that number. Let the next number be \[x\] . We know that the difference between \[x\] and \[8\] is two.
Thus, \[x - 8 = 2\] .
To find the value of \[x\] first let take \[ - 8\] to the other side.
 \[ \Rightarrow x = 2 + 8\]
On adding two and eight we will get the value of \[x\] .
 \[ \Rightarrow x = 10\]
Thus, the next number in the series is \[10\] . So, option (a) \[10\] is the correct answer.
Let us see the other option. Option (b) \[11\] cannot be the next number since the difference between \[11\] and \[8\] is \[3\] . Thus, option (b) cannot be the right answer.
Option (c) \[12\] cannot be the next number since the difference between \[12\] and \[8\] is \[4\] . Thus, option (c) cannot be the right answer.
Option (d) \[13\] cannot be the next number since the difference between \[13\] and \[8\] is \[5\] . Thus, option (d) cannot be the right answer.

So, the correct answer is “Option A”.

Note: We have found that the relation between the numbers in the given series is that the difference between any two consecutive numbers is two, we can also say that the given series is multiple of two. The first number in the series is \[2\] (i.e., \[1 \times 2 = 2\] ), second number is \[4\] (i.e., \[2 \times 2 = 4\] ), third number is \[6\] (i.e., \[3 \times 2 = 6\] ), fourth number is \[8\] (i.e., \[4 \times 2 = 8\] ), then the next number should be ( \[5 \times 2 = 10\] ) ten.