Puzzles/Easy Sequence 3/Solution

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a). The ascending powers of 2 are added to the previous number.

We start with 1 and add 2^0 to get 2, then add 2^2 (4) to get 6, plus 2^3 (8) equals 14, + 2^4=30, + 2^5=62

1, 2, 4, 6, 14, 30, . . .


b). The sequence in question is 1, 2, 6, 14, ... (without the 4). We can describe this sequence as follows:

         X(1):= 1 
         X(2):= 2 
         X(n)= 2*[X(n-2) + X(n-1)] - 2*(n-3)  (for n > 2)

We obtain: 1, 2, 6, 14, 36, 94, ...