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

Question
Sequences
asked 2021-01-15
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

Answers (1)

2021-01-16
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.
0

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