Question

What number should come next?
 $84{\text{ 78 72 66 60 54 48}}$
(A) $44{\text{ 34}}$
(B) $42{\text{ 36}}$
(C) $42{\text{ 32}}$
(D) ${\text{40 34}}$
(E) ${\text{38 52}}$

Answer 1

Hint: In these types of questions, we have to examine the numbers very carefully and then try to figure out any relation between them. This is called number series reasoning. This type of series is a sequential order of numbers that are arranged in such a way that each term in the series is obtained according to some specific rules. These rules can be based on mathematical operations.

Complete step-by-step solution:
A number sequence is a list of numbers that are linked by a definite rule. If we work out that rule, we can easily work out the next numbers in the sequence.
In this case, the given sequence of numbers is \[84{\text{ 78 72 66 60 54 48}}\].
If we look closely, we see that $84 - 6 = 78$ , $78 - 6 = 72$, $72 - 6 = 66$ and so on $54 - 6 = 48$ .
Hence, in this series, the next number is obtained by subtracting $6$ from the previous number.
Hence the difference between each pair of numbers in this series is given by $ - 6$ .
Therefore, to obtain the next number after $48$ , we subtract $6$ from $48$ .
Thus the number that should appear after $48$ must be $48 - 6 = 42$ .
Thus the series is continued and it becomes \[84{\text{ 78 72 66 60 54 48 42}}\].
Proceeding in the similar process, we should obtain the next number to appear after the number $42$ must be $42 - 6 = 36$ .
Hence we complete the series as \[84{\text{ 78 72 66 60 54 48 42 36}}\].
Thus the numbers that came next are \[{\text{42 36}}\].
Hence option $(B)$ is correct.

Note: This number series is called Arithmetic Progression(A.P.). It is defined as a sequence of numbers such that the difference between the consecutive numbers is constant. For example the sequence $2,5,8,11,14,17,...$ is an arithmetic progression with a common difference of $3$. The given problem is also an arithmetic progression having the common difference of $ - 6$.