CPM Homework Help : INT3 Problem 10-74

Use mathematical induction to prove that the relationship below is true for $n\ge1$ .

$9 + 13 + 17 + \ldots + ( 4 n + 5 ) = n ( 2 n + 7 )$

Step 1:

Prove the relationship is true for $n = 1$ .
$9 = \left(1\right)\left(2\left(1\right) + 7\right)$
$9 = 9$

Step 2:

Assume that the relationship is true for some number $k$ .

Step 3:

Prove that, if the relationship is true for $k$ , then it is true for $k + 1$ .