what is the nature of this sequence? $3, 4, 10, 33, 136$
what will be next most appropriate value?
I tried finding any relation in the sequence but i couldn't.
$a.276 $
$b.539 $
$c.612 $
$d.685$
 A: I agree with all the complaints about this sort of problem, but still.... There are some techniques which work from time to time. 
Try taking differences: $4-3=1$, $10-4=6$, $33-10=23$, $136-33=103$, so now we have to explain the sequence $1,6,23,103,\dots$. Hmm, that doesn't seem very helpful. 
OK, subtraction didn't work, try division: $4\div3=1r1$, $10\div4=2r2$, $33\div10=3r3$, $136\div33=4r4$ - hey, that looks much better! (When I write $arb$, I mean quotient $a$, remainder $b$.) 
A: I must say, I have always disliked 'find the next term in the series question'. For any sequence, it is easy to produce any number next (e.g. for a sequence of $n$ terms, pick the $n+1$ number and then fit a polynomial to those $n+1$ terms).
OEIS does not give anything useful for your sequence - how has it arisen?
Edit: For this question, as Moron has shown, the likely answer is 685, based on the sequence $3,3\times 1 + 1 = 4, 4 \times 2 + 2 = 10, 10 \times 3 + 3 = 33, 33 \times 4 + 4 = 136,$$136 \times 5 + 5 = 685$ . But in general knowing how to find the pattern in this sequence, will not help (much) in finding patterns in similar sequences.
