The recursive formula A(n) = A(n-1)+5 represents the amount of money in your savings account after n weeks. You start with $100. What is an explicit formula for the amount of money in your savings account after n weeks?A. A(n)=5+100(n−1)B. A(n)=100(n−1)−5C. A(n)=100+5(n−1)D. A(n)=5(n−1)−100

permaneceerc 2021-01-15 Answered

The recursive formula \(A(n) = A(n-1)+5\) represents the amount of money in your savings account after n weeks. You start with $100. What is an explicit formula for the amount of money in your savings account after n weeks?
A. \(A(n)=5+100(n−1)\)
B. \(A(n)=100(n−1)−5\)
C. \(A(n)=100+5(n−1)\)
D. \(A(n)=5(n−1)−100\)

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funblogC
Answered 2021-01-16 Author has 13375 answers

The recursive formula is for arithmetic sequence where A1 is the first term \((A1=100)\) and the common difference is \(d=5\).
The explicit formulf is given by: \(A(n)=A1+(n-1)d\)
So, we have: \(A(n)=100+(n-1)(5)\)
\(A(n)=100+5(n-1)\)
So, the correct answer is choice C.

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