Question

Select the recursive and explicit formula for the Arnold family 2 answers

Answer 1

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

$A(n)\text{ = a}_{n\text{ - 1}}\text{ }\times\text{ 2}$

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