Question

Look at this series : $1000,200,40...$What number should come next?
A) $8$
B) $10$
C) $15$
D) $20$

Answer 1

Hint: Hint: In the given series we have to find the next number in the series. The given series is a simple division series that we can understand easily. In this series, every number is divided by a particular common number for the end of the series. That means all the numbers are divided by the same number. Find the common number and we get the solution easily.
Formula used in the problem:
Common rule$ = \left( {\dfrac{{{1^{st}}number}}{x} = {2^{nd}}number} \right)\left( {\dfrac{{{2^{nd}}number}}{x} = {3^{rd}}number} \right)....$
$x = $The common number divides all numbers in the series.

Complete step-by-step solution:
In the given problem we have to find the next number in the given series.
The given series is $1000,200,40...$
First, we have to find the common number which divides all the numbers in series.
Using the common rule we can find the common number which divides all the numbers in the series
The first number is $1000$
The second number is $200$
Now apply the common rule,
$
  \dfrac{{1000}}{x} = 200 \\
  \dfrac{{1000}}{{200}} = x \\
  x = 5 \\
   = \dfrac{{40}}{5} \\
  8 \\
 $
Applying cross multiplication we have,
$\dfrac{{1000}}{{200}} = x$
Now divide the values, we get
$x = 5$
Hence the common number which divides all number is $5$
Therefore now we are going to find the fourth term of the series
By the common rule, the fourth term of the series is, divide by the third number by the common number five.
After the division we get the fourth term of the given series.
Now apply the common rule,
The third term is forty and the common number is 5
$ = \dfrac{{40}}{5}$
$ = 8$
Hence the fourth term of the given series is eight.
Hence option A is the answer.
The explanation for option B:
 By using the common rule we have found the answer is $ = 8$
Hence option B is not an answer.
An explanation for option C:
By using the common rule we find the fourth term is $8$.
Therefore option C is not an answer.
The explanation for option D:
 From the above complete solution, we find the answer is $8$.
Therefore option D is not a solution for this given problem.
Hence the solution is option A.

Note: In mathematics, there are four basic mathematical operations. There are addition, subtraction, multiplication, and division. The division is defined as the splitting of a large group into an equal smaller group.