A woman walks half a mile on the first Sunday and a quarter-mile more on each Sunday after. What is her total distance walked after 8 weeks?

1. The weekly distances form an arithmetic sequence with first term 1/2 and common difference 1/4. 2. The eighth term is a_8 = 1/2 + (1/4)(8 - 1) = 1/2 + 7/4 = 9/4. 3. Substitute into S_n = n(a_1 + a_n)/2 to get S_8 = 8(1/2 + 9/4)/2. 4. Inside the bracket, 1/2 + 9/4 = 11/4, so S_8 = 8(11/4)/2 = 22/2 = 11. 5. The total distance is 11 miles. 6. Reporting 9/4 alone would answer the distance in the eighth week rather than the running total, which is the trap here. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_