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After surgery, a woman walks 1 mile on the first Sunday and adds a quarter-mile every Sunday after that. What total distance has she walked after 8 Sundays?
A11 miles
B22 miles
C12 miles
D15 miles
Answer & Solution
Correct answer: D. 15 miles
1. The weekly distances form an arithmetic sequence with a_1 = 1 mile and d = 0.25 mile.
2. Find the eighth walk: a_8 = 1 + (8 - 1)(0.25) = 2.75 miles.
3. The total is the arithmetic series S_8 = 8(a_1 + a_8)/2.
4. S_8 = 8(1 + 2.75)/2 = 4 x 3.75 = 15 miles.
5. Option B, 22 miles, multiplies the last walk by 8, as if every Sunday matched the longest walk.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 SERIES AND THEIR NOTATIONS_
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