9514 1404 393
Answer:
a[1] = 3
a[n] = 2×a[n-1] +1
Explanation:
We observe the first differences are ...
7-3 = 4
15-7 = 8
31-15 = 16
63-31 = 32
The first differences increase by a factor of 2, so we expect the recursive formula will have a term that looks like "2×a[n-1]".
The second term is 2·3+1 = 7.
The third term is 2·7+1 = 15.
This suggests our recursive formula is ...
a[1] = 3
a[n] = 2×a[n-1] +1