Question

Find the missing number 3,3,6,18,72,360,?

Answer 1

Hint: The problem is simply based on number series. This series follows some patterns. Once we found or decoded the pattern the answer would be very easy to find. Now for this series above we can see that the next term is 1 times, two times , three times,…. Of the previous term respectively. There we go! Our last term would be six times its previous term.

Complete step by step solution:
We are given a series as 3,3,6,18,72,360,?
Now our duty is to find the pattern in the series.
Let’s take the first two terms 3 and 3.
The only clue we get is that the second term is \[ \times 1\] of the first term.
And also if we add 0 to 3 we get the answer as 3.
Now for the next two terms 3 and 6.
Now \[3 \times 2 = 6\]. So the pattern of the product is fit.
 Let’s check for the addition. Its \[3 + 3 = 6\]
Next are 6 and 18.
So \[6 \times 3 = 18\]. So the product works.
For addition, \[6 + 12 = 18\]
But we are not getting any chain or relation between the term for addition so we will drop it here only and will go with the product.
Thus,
\[3 \times 1 = 3\]
\[3 \times 2 = 6\]
\[6 \times 3 = 18\]
\[18 \times 4 = 72\]
\[72 \times 5 = 360\]
Now the term that will replace the question mark will be 6 times 360.
\[360 \times 6 = 2160\]
Thus the missing number is 2160.
Thus the series is 3,3,6,18, 72,360,2160.
So, the correct answer is “2160”.

Note: Note that these questions are totally based on logic. Sometimes the logic is clearly visible and sometimes it is hidden like it can be obtained in the second step method. But note that we should check for a particular pattern for the full series because sometimes it may change from second or last terms. So don’t just check for the initial terms only. Also try for all the possible logical combinations. Because sometimes there can be a common logic for two different problems.