Question

Find the 78th term of the arithmetic sequence 14, 5, -4, ...14,5,−4

Answer 1

`\bf 14~~,~~\stackrel{14-9}{5}~~,~~\stackrel{5-9}{-4}~~,~~...~\hspace{10em}\stackrel{\textit{common difference}}{d = -9} \\\\[-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}\\[-0.5em] \hrulefill\\ a_1=14\\ d= -9\\ n= 78 \end{cases} \\\\\\ a_(78)=14+(78-1)(-9)\implies a_(78)=14+(77)(-9) \\\\\\ a_(78)=14-693\implies a_(78)=-679`