f(n)=93+4(n-1) Complete the recursive formula of f(n). {:[f(1)=],[f(n)=f(n-1)+]:}

Establish Base Case: To find the recursive formula for the sequence, we need to express f(n) in terms of f(n-1). The given explicit formula is f(n)=93+4(n-1). Let's first find f(1) to establish the base case of the recursive formula. Calculation: f(1) = 93 + 4(1-1) = 93 + 4(0) = 93 + 0 = 93Find f(2): Now, let's find f(2) using the explicit formula to see the relationship between f(2) and f(1). Calculation: f(2) = 93 + 4(2-1) = 93 + 4(1) = 93 + 4 = 97Identify Recursive Relationship: We can see that f(2) is 4 more than f(1). This is because the sequence increases by 4 each time (as indicated by the +4 in the explicit formula). Therefore, the recursive formula will involve adding 4 to the previous term. Calculation: f(n) = f(n-1) + 4Recursive Formula: We have established the base case and the recursive step. The recursive formula for the sequence is: f(1) = 93 f(n) = f(n-1) + 4 for n > 1

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f(n)=93+4(n-1)
Complete the recursive formula of
f(n).

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

$f(n)=93+4(n-1)$ $\newline$ Complete the recursive formula of $f(n)$ . $\newline$ $\begin{array}{l} f(1)=\square \\ f(n)=f(n-1)+\square\\ \end{array}$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

f(n)=93+4(n-1)

\newline

Complete the recursive formula of

f(n)

\newline

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

Establish Base Case: To find the recursive formula for the sequence, we need to express $f(n)$ in terms of $f(n-1)$ . The given explicit formula is $f(n)=93+4(n-1)$ . Let's first find $f(1)$ to establish the base case of the recursive formula. $\newline$ Calculation: $f(1) = 93 + 4(1-1) = 93 + 4(0) = 93 + 0 = 93$
Find $f(2)$ : Now, let's find $f(2)$ using the explicit formula to see the relationship between $f(2)$ and $f(1)$ . $\newline$ Calculation: $f(2) = 93 + 4(2-1) = 93 + 4(1) = 93 + 4 = 97$
Identify Recursive Relationship: We can see that $f(2)$ is $4$ more than $f(1)$ . This is because the sequence increases by $4$ each time (as indicated by the $+4$ in the explicit formula). Therefore, the recursive formula will involve adding $4$ to the previous term. $\newline$ Calculation: $f(n) = f(n-1) + 4$
Recursive Formula: We have established the base case and the recursive step. The recursive formula for the sequence is: $\newline$ $f(1) = 93$ $\newline$ $f(n) = f(n-1) + 4$ for n > 1