A sequence with a1=1 is defined by the recurrence relation an+1=2nan for all natural numbers n. If a23=2p, then what is p?
For a23, n=22. We can set up the equation 222×a22=2p. We can see that a22=221×a21. We can keep doing this until we get: 222+21+20...+3+2+1×1=2p, so p=22+21+20...+3+2+1=253.
- Daisy
Thanks!