Puzzles/Number sequences

The task is to find the hidden principle that constructs the list, and sometimes to continue the sequence, which is indicated by a question mark. Be aware: some sequences are infinite, some are finite. If you find a different solution than the given one please add it to the solution page. Creativity is encouraged!

Easy sequences
1 2 4 8 ?                 solution 1 2 4 7 ?                 solutions (more than one) 3 9 27 81 ?               solution 2 3 5 8 13 21 ?           solution 1 0 1 0 1 0 1 1 0 1 0 1   solution 2 3 6 7 1 9 4 5 8         solution 0 1 1 1 1 1 1 ...         solution

Medium Sequences
1 3 7 61 ?                solution 2 -2 0 2 -3 0 ?           solution 1 4 1 5 9 ?               solution

Hard Sequences
??               85  90              29  67   0    solution 83 33  69   2           1  81  91  57  36        60  55  61  29  35   6      29  42  45  23  13   5  16    23  13  44   7  39  69  47  98  61  41  91  82   1  37  27  71  36 6   4   6   9   0   8   9   5   9   6

??               73  94              69  81  28    solution 56  3  43  54          33  98  49  91   8         7  31  44  27  57   6      26  45  71  38  61  65  88    25  36   7  97  76  91  87  86  83  55  98   1   5  10   1  15  96 3   9   3   4   4   3   0   7   5   6