1. Since the equation we are going to use to prove this statement, that is, the equation br = 5br-1 - 6br-2, relates br to two previous terms in the sequence, we shall need two statements in our basis step.
2. Let P(n) be the claim that bn = 2n
for all integers n1.
Since the equation we are going to use to prove this statement, that is, the equation br
= 5br-1 - 6br-2, relates br to two previous terms in the
sequence, we shall need two statements in our basis step.
P(1) is the statement: b1 = 21 and P(2) is the statement:b2 = 22 .
P(i) is the statement: bi = 2i .
P(k) is the statement: bk = 2k .
For a proof by strong mathematical induction, you first need to check that all the statements in your basis step (P(1) and P(2)) are true. Then assume that P(i) is true for all values of i where 1 < i < k and use this to show that P(k) is true.