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2, 6, 18...

That is a sequence of patterns.

A sequence usually has a pattern. You just have to find out what is the pattern and you can easily determine the next number which will come in the sequence.

Notice carefully and see that each number in the sequence is multiplied by 3 and that very number falls next in the sequence.

the first number in the sequence - 2
multiply with 3 - 2 × 3 , it's 6

and so the next number in the sequence is 6..

now, 6
multiply with 3 - 6 × 3 , it's 18

and so the next number in the sequence is 18..

THEREFORE, we get a series of number each multiplied by 3 -
2, 6, 18, ?

We figured out the pattern. Be sured by observing the numbers.
Now, the only thing left to find out is the number that will come next.

Work with the pattern you have discovered. This is why, pattern had to be found out, first. Until now, you must have been wondering that what was the need of finding the pattern.

The pattern is : each number in the sequence is multiplied by 3 and that very number falls next in the sequence

Multiply 18 by 3, and you get (18 × 3) = 54 .
Yes!!! We found that very number which we were struggling so long for.

You got it right. The next number n the sequence is 54. We get the complete sequence - 
2 , 6 , 18 , 54

You can find out further numbers in the sequence by making use of the pattern. Now, you understand how important the pattern is. 

You want to go further? Then, go : 

Multiply 54 by 3, you get 162.
Then , (162 × 3) = 486
(486 × 3).....and all

Until then, Au Revoir (french for goodbye).
Ta ta ta ... bye ...

1 5 1
The next number should be 34.
if we break the series we get, 2(1 3 9 17)
notice that the difference between 1 and 3 is 2(actually 2×1) , 3 and 9 is 6 ( actually 2×3) so the next number will be 17 as the difference between 9 and 17 is 8 (actually 2×4).
1 2 1
i cannot rate it now as i am using my phone
oh !!
i think you did wrong calculation..
first difference is 2×1 ...second is 2×3 then third must be 2×5 ...plz check your answer