Chapter 11 - 11.2 - Arithmetic Sequences and Partial Sums - 11.2 Exercises - Page 786: 27

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

The $nth$ term of an arithmetic sequence is given by: $a_n=a_1+(n-1)d$ If $a_1=5,~~a_4=15$: $a_4=a_1+(4-1)d$ $15=5+3d$ $10=3d$ $d=\frac{10}{3}$ $a_n=5+(n-1)(\frac{10}{3})=\frac{5(3)}{3}+\frac{10}{3}n-\frac{10}{3}=\frac{10n+5}{3}$ $a_n=\frac{10n+5}{3}$