Question

a movie theater has 180 seats how many rows of seats does it have if the first row has 12 seats after has two more seats than the previous row

Answer 1

The aritmetic sequence is represented by the following expression,

`\begin{gathered} a_n=a+(n-1)d\text{ } \\ a_{_n=\text{ nth term }} \\ a=\text{ first term} \\ n_{=\text{ the position of the term}} \\ d=\text{ common difference} \\ \end{gathered}`
`180=\text{ 12 + (n-1)2}`

Solve for n,

`\begin{gathered} (180-12)/(2)=\text{ n-1} \\ 84=\text{ n-1} \\ n=85_{} \end{gathered}`