Chapter 11 - Further Topics in Algebra - 11.2 Arithmetic Sequences and Series - 11.2 Exercises - Page 1024: 25

$a_n=\frac{10}{3}n+\frac{5}{3}$ $a_8=\frac{85}{3}$

$a_1=5, a_4=15$ Find $d$: $a_n=a_1+(n-1)d$ $a_n=a_1+(4-1)d$ $15=5+3d$ $10=3d$ $d=\frac{10}{3}$ $a_n=a_1+(n-1)d$ $a_n=5+(n-1)*\frac{10}{3}$ $a_n=5+\frac{10}{3}n-\frac{10}{3}$ $\boxed{a_n=\frac{10}{3}n+\frac{5}{3}}$ $a_8=\frac{10}{3}*8+\frac{5}{3}$ $a_8=\frac{80}{3}+\frac{5}{3}$ $\boxed{a_8=\frac{85}{3}}$