State the next term of each sequence
a) 1, 16, 81,
b) 1, 1, 2, 4, 7, 13,

A) 1, 16, 81, and 256 are all perfect squares. Find their squares:
1, 4, 9, 14.
In this sequence, you first at 3, then 5, then 7. So, logically, you would add 9 next. 14 + 9 is 23, and 23 squared is 529.
b) I'm not sure the data points for this sequence are correct. I'd have to guess 42 based on this difference chart:
1    1    2     4     7     13     24   42
  +0  +1  +2    +3   +6   +11  +18
      +1  +1  +1    +3   +5   +9
         +0  +0   +2   +2   +4
            +0   +2  +0   +2

A)


b)