Question

1. write an explicit and recursive rule for the arithmetic sequence 92, 72, 52, 32, ...

$f(1) =$

$d =$

explicit: $f(n) =$

recursive: $f(n) =$

$f(1) =$

Explanation:

Step1: Identify first term

$f(1) = 92$

Step2: Calculate common difference

$d = 72 - 92 = -20$

Step3: Derive explicit formula

Use arithmetic sequence formula $f(n)=f(1)+(n-1)d$
$f(n) = 92 + (n-1)(-20) = 92 -20n +20 = 112 -20n$

Step4: Derive recursive formula

Recursive rule uses prior term: $f(n)=f(n-1)+d$, with base case
$f(n) = f(n-1) - 20$, where $f(1)=92$

Answer:

$f(1) = 92$
$d = -20$
Explicit: $f(n) = 112 - 20n$
Recursive: $f(n) = f(n-1) - 20$
$f(1) = 92$