### Home > INT3 > Chapter 10 > Lesson 10.1.5 > Problem10-74

10-74.

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

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

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

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

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