Question

Write an explicit formula for a_na

n
​
, the n^{\text{th}}n
th
term of the sequence 2, 4, 6, ...2,4,6,....

Answer 1

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