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A five-year-old receives a $2 weekly allowance, and each year it rises by $3 per week, so after n years the allowance is A_n = 2 + 3n dollars. What is the weekly allowance at age 12?
A$23 per week
B$38 per week
C$21 per week
D$26 per week
Answer & Solution
Correct answer: A. $23 per week
1. The formula counts years after age five, so first find n = 12 - 5 = 7.
2. Substitute n = 7 into A_n = 2 + 3n.
3. A_7 = 2 + 3(7) = 2 + 21 = 23 dollars per week.
4. So the allowance at age 12 is $23 per week.
5. Option B, $38, comes from plugging in n = 12 directly and skipping the subtraction of the starting age.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 ARITHMETIC SEQUENCES_
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