Question

Write a recursive rule for the sequence:
1,2,12,56,272...
and
2,5,11,26,59...
and
-3,-2,5,-3,-2...
I can't find the pattern in these and am unsure on how to write the rule.
Thanks

Answer 1

Well, let's see.
#1:
1*1
2*1
4*3
8*7
16*17 Hmmm

2^1-1
2^2-2
2^4-4
2^6-8
2^8+16 Hmmm

#2:
2
2*2+1
2*5+1
2*11+5
2*26+7 Hmmm

2^2-2
2^3-3
2^4-5
2^5-6
2^6-5 Hmmm.

#3: clearly -3,-2,5 repeats as a sequence

Sorry. I can't seem to get #1 and #2 right off. They almost follow a pattern, but then veer off. Anyone else?

Answer 2

For the last one it should be
a sub 1 = -3
a sub 2 = -2
a sub n = -((a sub n-2) + (a sub n-1))

Answer 3

The first one is
Asub1=1
Asub2=2
A subn= 4*(asubn-2+asubn-1)