Question

State the next term of each sequence
a) 1, 16, 81, 256....
b) 1, 1, 2, 4, 7, 13, 24....

Answer 1

a)

`1,16,81,256,\underline{625}\\ \text{The general formula is } n^4 \text{ where } n\in \mathbb{N}`

b)

`1,1,2,4,7,13,24,\underline{44}\\ \text{Each number is the sum of three preceding numbers.}`

Answer 2

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