Identify given parameters

We are provided with the first term $a = 36$, the last term $l = 46$, and the total sum $S = 574$.

$a = 36, l = 46, S = 574$

Set up the sum formula

The sum of an Arithmetic Progression given the first and last terms is given by the formula $S = \frac{n}{2}(a + l)$.

$574 = \frac{n}{2}(36 + 46)$

Calculate the number of terms

Simplify the sum of the terms inside the parentheses: $36 + 46 = 82$. Then, $574 = \frac{n}{2} \times 82$, which simplifies to $574 = n \times 41$. Solving for $n$ gives $n = \frac{574}{41} = 14$.

$n = 14$