Question

the first five terms of an arithmetic sequence are -1,3,7,11,15. write down, in terms of n, an expression for the nth term in this sequence

Answer 1

$-1~~,~~\stackrel{-1+4}{3}~~,~~\stackrel{3+4}{7}~~,~~\stackrel{7+4}{11}~~,~~\stackrel{11+4}{15}\qquad \qquad \stackrel{\textit{common difference}}{d = 4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{-1}\\ d=\stackrel{\textit{common difference}}{4} \end{cases}\implies a_n=-1+(n-1)4 \\\\\\ a_n=-1+4n-4\implies a_n=4n-5$