Question

Write an equation for the nth term of the arithmetic sequence 12,14,16,18

Answer 1

$\bf 12~~,~~\stackrel{12+2}{14}~~,~~\stackrel{14+2}{16}~~,~~\stackrel{16+2}{18}\qquad \qquad \stackrel{\textit{common difference}}{d = 2} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=12\\ d = 2 \end{cases} \\\\\\ a_n=12+(n-1)2\implies a_n=12+2n-2\implies a_n=2n+10$