Writing rules for sequences often requires a bit of creative thinking. Sometimes it helps to look a the differences between terms. After you have computed differences, you can compare them to constants, or terms in the sequence, or check to see if they have some sequence of their own. Sometimes the sequence is constructed so it has a pattern that is replicated over and over.
12. Differences are 5, 3, 8, 11. We see that the last of these correspond exactly to terms in the sequence. In fact, it appears that each term in the sequence is the sum of the previous two. Then the recursion relation is
... a[1] = 3
... a[2] = 8
... a[n] = a[n-1] + a[n-2]
_____
13. It appears that each term of the sequence is the opposite of the term 3 before it.
... a[1] = 1
... a[2] = 2
... a[3] = 1
... a[n] = -a[n-3]
