### Home > A2C > Chapter 12 > Lesson 12.3.1 > Problem12-137

12-137.

Prove $5 + 8 + 11 + \ldots + ( 3 n + 2 ) = \frac { n ( 3 n + 7 ) } { 2 }$by induction.

Verify that it is true for n = 1.

$5=\frac{(1)(3(1)+7)}{2}$

$5 = 5$

Assume that the identity is true for some arbitrary number $k$.

Prove that given the above assumption, the identity holds true for $\left(k + 1\right)$.