Question

Write an explicit formula for a_na

n
​
, the n^{\text{th}}n
th
term of the sequence 35, 42, 49, ...35,42,49,....

Answer 1

`35~~,~~\stackrel{35+7}{42}~~,~~\stackrel{42+7}{49}~~,~~....~\hspace{10em}\stackrel{\textit{common difference}}{d=7} \\\\[-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}}{35}\\ d=\stackrel{\textit{common difference}}{7} \end{cases} \\\\\\ a_n=35+(n-1)(7)\implies a_n=35+(7n-7)\implies a_n=7n+28`