Proof by Induction

[mendhak]

What is "Induction Hypothesis"?

This question has me stumped, any help?

We define the sequence L by L₀=5 and for k>=1,
L_k=2L_k-1-7.

a) Determine L₄ <--- This one I got.. duh

b) Prove by induction that L_k= 7-2^k+1

I can't figure out b. Any help appreciated. Thanks.