Question

What is a value of the 13th term of the sequence -7 negative 3 1 5?

Answer 1

`\bf -7~~,~~\stackrel{-7+4}{-3}~~,~~\stackrel{-3+4}{1}~~,~~\stackrel{1+4}{5}~~,.....`

so, it's really adding 4 to get the next term, namely, 4 is the common difference, and the first term is -7.

`\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\\ a_1=-7\\ d=4\\ n=13 \end{cases} \\\\\\ a_(13)=-7+(13-1)4\implies a_(13)=-7+48\implies a_(13)=41`