Answer: The first and last options are correct
Explanation:
The recursive formula is written in terms of the previous term of the sequence. From the information given,
the Arnold's are going to save a nickel on the first day of the month and double the amount each day of the month. Thus, the recursive formula would be
[tex]A(n)\text{ = a}_{n\text{ - 1}}\text{ }\times\text{ 2}[/tex]
where
an - 1 defines a previous term
To write the explicit formula, we would apply the formula for finding the nth term of an arithmetic sequence which is expressed as
An = ar^(n - 1)
where
a is the first term of the sequence
n is the number of terms
r is the common ratio between consecutive terms
Thus,
r = 2 because the amount is doubling each day
n = number of days
a = value of 1 nickel = $0.05
By substituting these values into the formula,
the explicit formula is
A(n) = 0.05(2)^n - 1
