Chain of numbers

This task is about continuing number patterns and finding a rule.
A chain of numbers begins: 1  3
This could be continued several ways.
 
a)
1  3  5  7  9
 
What is the rule for continuing this chain? ____________________________________
 
b)
1  3  9  27  81
 
What is the rule for continuing this chain? ____________________________________
 
c)
1  3  7  15  31  63
 
What is the rule for continuing this chain? ____________________________________
 
d) i)
Make up a different chain by writing down the next three numbers.
The chain starts with: 1  3 and keeps getting bigger.
 
1 3      
 
  ii) Write the rule for the chain you have written.