Answer
See below.
Work Step by Step
The difference between two terms with an index difference of $13$ is $65$, thus $d=65/13=5$. Thus $a_1=a_{7}-(7-1)d=31-6(5)=1$.
The nth term of an arithmetic sequence can be obtained by the following formula: $a_n=a_1+(n-1)d$, where $a_1$ is the first term and $d$ is the common difference.
Hence here: $d=5,a_1=1,a_{n}=1+(n-1)(5)=-4+5n$