Question

the first row an auditorium has 24 seats. the second row has 28 seats, and the third row has 32 seats. if this patterns continues, how many seats are in the 20th row?

Answer 1

$\bf 24~~,~~\stackrel{24+4}{28}~~,~~\stackrel{28+4}{32}.....\qquad \stackrel{\textit{common difference}}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=24\\ d=4\\ n=20 \end{cases} \\\\\\ a_{20}=24+(20-1)4\implies a_{20}=24+76\implies a_{20}=100$

Answer 2

D the answer (i'm pretty sure) is D