# 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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## Expert Answer

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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