Question

An arithmetic sequence with a third term of 8 and a constant difference of 5

Answer 1

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ \hrulefill\\[0.5em] a_3=8\\ n=3\\ d=5 \end{cases} \\\\\\ a_3=a_1+(3-1)5\implies 8=a_1+(2)5 \\\\\\ 8=a_1+10\implies -2=a_1 \\\\\\ \begin{cases} a_1=-2\\ d=5 \end{cases}\implies a_n=-2+(n-1)d$