Question

Find a16 of the sequence 1,6,11,16

Answer 1

$\bf 1~~,~~\stackrel{1+5}{6}~~,~~\stackrel{6+5}{11}~~,~~\stackrel{11+5}{16}...\qquad \qquad \stackrel{\textit{common difference}}{d=5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=1\\ d=5\\ n=16 \end{cases} \\\\\\ a_{16}=1+(16-1)5\implies a_{16}=1+(15)5\implies a_{16}=76$