10
QuizMultiple Choice

Simple Interest and Arithmetic Sequences — Quiz

Question 10 • Advanced Financial Algebra

Victor has been paying off his student loan with consistent payments. Over the past few years, his remaining loan balances were $⁢10,000 , $⁢9,500 , $⁢9,000 , $⁢8,500 , $⁢8,000 , ... What is the formula for the arithmetic sequence that represents the decreasing balances of Victor's student loan?

Answer
A
an=10,500−500⁢(n−1)
B
an=10,000−500⁢n
C
A sub n is equal to 10 comma 500 plus 500 n
D
an=10,000−500⁢(n−1)

Explanation

The first balance is $10,000, and each balance decreases by $500, so the common difference is −$500. Using the arithmetic sequence formula aₙ = a₁ + (n − 1)d gives aₙ = 10,000 − 500(n − 1). This is choice D, “aₙ = 10,000 − 500(n − 1).”

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