f(n)=41-5n Complete the recursive formula of f(n). {:[f(1)=],[f(n)=f(n-1)+]:}

Write Explicit Formulas: To find the recursive formula for the sequence, we need to express f(n) in terms of f(n-1). Let's start by writing down the explicit formula for f(n) and f(n-1). f(n) = 41 - 5n f(n-1) = 41 - 5(n-1)Simplify Expression: Now, let's simplify the expression for f(n-1) to see the relationship between f(n) and f(n-1). f(n-1) = 41 - 5(n-1) f(n-1) = 41 - 5n + 5 f(n-1) = (41 - 5n) + 5 f(n-1) = f(n) + 5Rearrange Equation: We can now rearrange the equation to solve for f(n) in terms of f(n-1). f(n) = f(n-1) - 5 This is the recursive formula for the sequence.

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f(n)=41-5n
Complete the recursive formula of
f(n).

{:[f(1)=],[f(n)=f(n-1)+]:}

$f(n)=41-5 n$ $\newline$ Complete the recursive formula of $f(n)$ . $\newline$ $\begin{array}{l} f(1)=\square \\ f(n)=f(n-1)+ \end{array}$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

f(n)=41-5 n

\newline

Complete the recursive formula of

f(n)

\newline

\begin{array}{l} f(1)=\square \\ f(n)=f(n-1)+ \end{array}

Write Explicit Formulas: To find the recursive formula for the sequence, we need to express $f(n)$ in terms of $f(n-1)$ . Let's start by writing down the explicit formula for $f(n)$ and $f(n-1)$ . $\newline$ $f(n) = 41 - 5n$ $\newline$ $f(n-1) = 41 - 5(n-1)$
Simplify Expression: Now, let's simplify the expression for $f(n-1)$ to see the relationship between $f(n)$ and $f(n-1)$ .
$f(n-1) = 41 - 5(n-1)$
$f(n-1) = 41 - 5n + 5$
$f(n-1) = (41 - 5n) + 5$
$f(n-1) = f(n) + 5$
Rearrange Equation: We can now rearrange the equation to solve for $f(n)$ in terms of $f(n-1)$ .
$f(n) = f(n-1) - 5$
This is the recursive formula for the sequence.