Question

Complete the recursive rule and an explicit rule for the arithmetic sequence described by the table.

Month n 1 2 3 4 5
Account Balance ($) f(n) 35 32 29 26 23

f(1) =
A) 35
B) 29
C) 23
D) 32

The common difference is
A) 3
B) 2
C) 1
D) 4

The recursive rule is f(1) =
A) f(n) = f(n-1) - 3
B) f(n) = f(n-1) - 1
C) f(n) = f(n-1) - 4
D) f(n) = f(n-1) - 2

The explicit rule is f(n) =
A) f(n) = 38 - (n-1)
B) f(n) = 36 - (n-1)
C) f(n) = 37 - (n-1)
D) f(n) = 39 - (n-1)

Answer 1

The initial term (f(1)) of the arithmetic sequence is $35, and the common difference is $3. The recursive rule is f(n) = f(n-1) - 3. The explicit rule is f(n) = 38 - 3n.

Step-by-step explanation:

To answer the question, we need to identify the initial term and common difference of the arithmetic sequence given by the account balances for each month. Looking at the table:

It's clear that each month, the account balance is decreasing by $3, which is the common difference. Now, we can create the recursive and explicit rules.

Recursive Rule

The recursive rule for an arithmetic sequence is defined by the initial term and the common difference:

f(1) = 35

f(n) = f(n-1) - 3

Explicit Rule

For the explicit rule, we use the formula for an arithmetic sequence:

f(n) = f(1) + (n - 1)d

Which in this case translates to:

f(n) = 35 - 3(n - 1)

Therefore, the explicit rule is f(n) = 38 - 3n.