Induction

Suppose that we want to prove that for every integer $n$

$$1 + 6 + 11 + 16 + ... + (5n-4) = {n(5n-3) \over 2}$$A student writes the following outline for the proof of induction:

Assume that

$$1 + 6 + 11 + 16 + ... + (5k-4) = {k(5k-3) \over 2}$$

You aim to prove that

$$1 + 6 + 11 + 16 + ... +(5k-4) + (5(k+1)-4) = {(k+1)(5(k+1)-3) \over 2}$$You can do this by substituting our result for $n=k$

$${k(5k-3) \over 2} + (5(k+1)-4) = {(k+1)(5(k+1)-3) \over 2}$$And then you can use algebra to get both the sides to the same form.

The student missed a step. Write down the name of the missing step.