Question

The first 5 terms of a number pattern are shown below.

4, 9, 14, 19, 24

Which expression is equivalent to the value of the nth term in the pattern?

Answer 1

`\bf 4~~,~~\stackrel{4+5}{9}~~,~~\stackrel{9+5}{14}~~,~~\stackrel{14+5}{19}~~,~~\stackrel{19+5}{24}\qquad \impliedby \stackrel{\textit{common difference}}{d=5} \\\\[-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=4\\ d=5 \end{cases} \\\\\\ a_n=4+(n-1)5\implies a_n=4+5n-5\implies a_n=5n-1`