Question

Find the 59th term of the following arithmetic sequence. 15, 23, 31, 39

Answer 1

`15~~,~~\stackrel{15+8}{23}~~,~~\stackrel{23+8}{31}~~,~~\stackrel{31+8}{39}~~,~~...~\hspace{10em}\stackrel{common~difference}{d=8} \\\\[-0.35em] ~\dotfill\\\\ n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^(th)\ term\\ n=\stackrel{\textit{term position}}{59}\\ a_1=\stackrel{\textit{first term}}{15}\\ d=\stackrel{\textit{common difference}}{8} \end{cases} \\\\\\ a_(59)=15+(59-1)8\implies a_(59)=15+472-8\implies a_(59)=479`