Question

Find the 92nd term of the arithmetic sequence -29, -22, -15, ...

Answer 1

`-29~~,~~\stackrel{-29+7}{-22}~~,~~\stackrel{-22+7}{-15}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{d=+7} \\\\[-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=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-29\\ n=92\\ d=7 \end{cases} \\\\\\ a_(92)=-29+(92-1)7\implies a_(92)=-29+637\implies \boxed{a_(92)=608}`