Question

what should comme in'?' the number seris 51,61,84,?,165,221

Answer 1

It is really interesting question. A superb level number series .
Series is given, 51 , 61 , 84 , ? , 165 , 221
Now, Let see how to solve it ,
51----(+10) ----61 -----(+23) ----- 84----(+35)----$\bf{\boxed{119}}$---(+46)---165--------(+56)-----221
why I take 35 ,
Let's see 2nd series include in difference of given terms in series.
10---(+13)----23----(+12)----35----(+11)----46-----(+10)----56

Hence, unknown number is 119.
For better understanding , a rough daigram is shown in attachment.