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### Toughest Series Puzzle

Toughest Series Puzzle - 12 September

What is the next number in this series?

4,12,84,3612....

1. 62,4867 may be the solution..

2. 4 12 42 3612 6526884 21300113901612

4. 4, 4*(6/2), 12*(14/2), 84*(86/2), 3612*(3614/2).....
i.e.
4, 12, 84, 3612, 6526884......

5. 6541332.
4*(prime just greater than 4/2 )=12
similarly 12*7=84
84*43=3612
3612*1811=6541332

6. (12*12)/2+12=84
(84*84)/2+84=3612
(3612*3612)/2+3612=6526884

7. 3612*367 = 1325604

It is something like this
4*3=12
12*((12+2)/2))=84
84*((84+2)/2))=3412
3412*((3412+2)/2)=6526884
I hope you have got it..

9. 4 12 84 3612

4 * 2 = 8
4 * 1 = 4

84 is the third number

Again
12 * 3 =36
12 * 1=12

3612 Fourth number

In the same way

84 * 4=336
84 * 1=84

33684

Multiples of 21 ,31 ,41 n son on

10. It could also be solved as:-

4,12,84,3612,(1556772)

let us see how.

4*3=12
12*[3*(2)+1]=84
84*[7*(6)+1]=3612
3612*[43*(10)+1]=1556772

The pattern may be difficult to recognise hence I state it as 2,6,10 being the constant multiplier of previous successor term.
(Shrohan Mohapatra,Bhubaneswar,Odisha)

11. 4x3 = 12
12x7 = 84 (12 is last no. and 3x3-2=7)
84x43 = 3612 (84 is last no. and 7x7-6 = 43)
next no:
3612x(43x43-42)=6526884

12. next num = num*(num/2+1)
4 x((4/2)+1) =4 x 3 =12
12 x((12/2+1) =12 x 7 =84
84 x((84/2)+1) =84 x 43 =3612
3612 x((3612/2)+1)
= 3612 x 1807 =6526884

1. 4,12,84,3612......
ANS :-
2*2 , 2*2*3, 2*2*3*7, 2*2*3*7*43,......
as you can easily notice that the product of previous terms are repeating...
now, we can deduce a series from it for ease
i.e.
1,3,7,43....
By solving this,
((2nd term * 1st term) *2) +1
by this,
(3*1)*2 +1 = 7
similarly
(7*3)*2 +1 = 43
so,
(43*7)*2+1 = 602

Now the complete series answer is
2*2*3*7*43*602= 2174424