Question

The first and thirteenth terms of an arithmetic sequence are $\frac79$ and $\frac45$, respectively. What is the seventh term

Answer 1

$\text{Given:} \\a_1=\frac79 \\ a_{13}=a_1+12d=\frac79+12d=\frac45 \\ \\\text{Find:} \\ a_7=a_1+6d$

Upon solving for d and substituting it into $a_7$

$d=\frac{1}{45 \times 12}\\\\a_7=\frac79+\frac{6}{45 \times 12}=\frac79+\frac{1}{90}=\frac{71}{90}$