Question

Find the 85th term of the arithmetic sequence - 25, 37, 49, ...

Answer 1

`\bf -25~~,~~\stackrel{-25-12}{-37}~~,~~\stackrel{-37-12}{-49}~~,~~...\qquad \qquad \qquad \stackrel{\textit{common difference}}{d = -12} \\\\[-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=-25\\ d= -12\\ n = 85 \end{cases}`

`\bf a_(85)=-25+(85-1)(-12)\implies a_(85)=-25+(84)(-12) \\\\\\ a_(85)=-25+(-1008)\implies a_(85)=-25-1008\implies a_(85)=-1033`