Question

Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a14.

Answer 1

`\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}`

so, as you can see, the common difference is then -2, and the first term is clearly 8, thus

`\bf 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=8\\d=-2\\n=14\end{cases}\\\\\\a_(14)=8+(14-1)(-2)\implies a_(14)=8-26\implies a_(14)=-18`