Question

The sequence is 2, 10, 18, .... what is the 24th term?

Answer 1

`\bf 2~~,~~\stackrel{2+8}{10}~~,~~\stackrel{10+8}{18}~\hspace{7em}\stackrel{\textit{so the common difference is}}{d=8} \\\\[-0.35em] ~\dotfill\\\\ 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=2\\ d=8\\ n=24 \end{cases} \\\\\\ a_(24)=2+(24-1)8\implies a_(24)=2+(23)8 \\\\\\ a_(24)=2+184\implies a_(24)=186`