CPM Homework Help : A2C Problem 12-93

Use mathematical induction to prove that the relationship below is true for $n ≥ 1$ .

$9 + 14 + 19 + … + \left(4n + 5\right) = n\left(2n + 7\right)$

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 $k + 1$ .