Number Pattern(homework)

maximal_ideal_space , STEVIE-G™ , think more, you can also do!

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(a)
6=4+2
14=6+8=6+2^3
46=14+32=14+2^5
174=46+128=46+2^7

so the next term should be 174+2^9=174+512=686.

(b)
16=12+2^2
32=16+2^4
96=32+2^6
352=96+2^8

so the next term should be 352+2^10=1376.

Unfortunately, there are no particular method to do this kind of questions. All one can do is try and error, try any pattern you can think of that fit the observed pattern. For example, for this two questions, I try some patterns I can think of, then at last I tried calculating the difference of two adjecent terms, and discovered that they are all powers of 2, and hence I get the answer. There is no logical procedure at all !!! (滴汗!)