[tex]\text{Given:} \\a_1=\frac79 \\ a_{13}=a_1+12d=\frac79+12d=\frac45 \\ \\\text{Find:} \\ a_7=a_1+6d[/tex]
Upon solving for d and substituting it into [tex]a_7[/tex]
[tex]d=\frac{1}{45 \times 12}\\\\a_7=\frac79+\frac{6}{45 \times 12}=\frac79+\frac{1}{90}=\frac{71}{90}[/tex]
