Pattern Recognition -1

Can you find the number pattern/series which is NOT the regular number series (1, 2, 3, 4………) where the value of the n^th element will be n when n is an even number. For example 10^th element in the series will be 10. 100^th element will be 100.  1200^th element will be 1200. But 101^st element will not be 101. 123^rd element will not be 123.

 

 Answer :

Well, This was my idea. Very simple.

The pattern is a mix of two number series.

If we take regular number series 1,2,3,4,5…….  We can divide that in to two patterns.

1. Odd number pattern 1,_,3,_,5……
2. Even number pattern _,2,_,4,_6,_..........

Now let us keep the second pattern as it is and let us change the first pattern, the odd series like this 1*2,3*2,5*2………
2,6,10,…….. again there is a pattern…

Now the combined pattern is 2, 2, 6, 4, 10,6,………  nth element will be n always when n is an even number.

We can create so many pattern series like this which fits to the given criteria. Is not it?

But some body at office came up with the following single series
n*(-1)^n 
^ denotes power of

That is an excellent answer.:)