Question

Write an explicit formula for a_na

n
​
, the n^{\text{th}}n
th
term of the sequence 8, 2, -4, ...8,2,−4,....

Answer 1

`8~~,~~\stackrel{8-6}{2}~~,~~\stackrel{2-6}{-4}~~,~~....~\hspace{10em}\stackrel{\textit{common difference}}{d=-6} \\\\[-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=\stackrel{\textit{first term}}{8}\\ d=\stackrel{\textit{common difference}}{-6} \end{cases} \\\\\\ a_n=8+(n-1)(-6)\implies a_n=8+(-6n+6)\implies a_n=14-6n`