Question

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

Answer 1

Answer:

The 85 term of the arithmetic sequence would be 983

Step-by-step explanation:

Use the formula: an=a1+(n−1)d

an=a1+d(n-1)

a85= -25+(85-1)12

a85= -25+1008

a85=983

Answer 2

$\bf -25~~,~~\stackrel{-25-12}{-37}~~,~~\stackrel{-37-12}{-49}~~,~~...\qquad \qquad \qquad \stackrel{\textit{common difference}}{d = -12} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-25\\ d= -12\\ n = 85 \end{cases}$

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