As per the given question,

7 , 17 , 41 , 85 , ?  , 257

Take difference between given  number  

17-7 = 10,

41 - 17 = 24,

85 - 41= 44

Hence, series will be as per the given,

10, 24, 44 .....

Again taking the difference of the given term of the series with the next term.

24 -10 =14,

44 - 24 = 20 .... as so on.

Hence the required series will be 14, 20, 26, 32 ......     

Then 44 + 26 = 70

so our series 

7, 17 , 41, 85, 155 , 257    

= 155 Ans