Chapter 11 - 11.2 - Arithmetic Sequences and Partial Sums - 11.2 Exercises - Page 786: 43

$a_7=\frac{31}{8}$

$a_1=\frac{1}{8},~~a_2=\frac{3}{4}$ $d=a_2-a_1=\frac{3}{4}-\frac{1}{8}=\frac{3(2)}{4(2)}-\frac{1}{8}=\frac{6}{8}-\frac{1}{8}=\frac{5}{8}$ $a_n=a_1+(n-1)d$ $a_7=\frac{1}{8}+(7-1)\frac{5}{8}=\frac{1}{8}+6\frac{5}{8}=\frac{1}{8}+\frac{30}{8}=\frac{31}{8}$