Question

7, 16, 25, 34, 43, ..... nth term is

Answer 1

`\bf 7~~,~~\stackrel{7+9}{16}~~,~~\stackrel{16+9}{25}~~,~~\stackrel{25+9}{34}~~,~~\stackrel{34+9}{43}`

so, as we can see, we're really adding 9 to the current term, to get the next term, therefore, 9 is the common difference, and of course 7 is the first term.

`\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}\\[-0.5em]\hrulefill\\d=9\\a_1=7\end{cases}\\\\\\a_n=7+(n-1)9`