Find the number?

The series is -

12,12,18,45,180,1170,?

What's the next number in above series?






Ans.

Yep, my answer matches with that of bayazidahmed, 12285.

Here's the solution:

Lets name the general term of the sequence T(n)

The sequence (say R(n)) where R(n)=T(n+1)/T(n)
is 1,1.5,2.5,4,6.5...

The sequence (say S(n)) where S(n)=R(n+1)-R(n)
is 0.5,1,1.5,2.5....


Thus S(n) can be thought of a Fibonacci style sequence where S(n)=S(n-1)+S(n-2)
Considering this relation, the next term in S(n) would be 1.5+2.5=4

Considering this, the next term in R(n) would be 6.5+4=10.5

Thus the next term in T(n)=1170*10.5 = 12285