f(n)=-11+22(n-1) Complete the recursive formula of f(n). {:[f(1)=◻],[f(n)=f(n-1)+]:}

Identify First Term: Identify the first term of the sequence using the given explicit formula. The explicit formula is f(n)=-11+22(n-1). To find the first term, f(1), we substitute n=1 into the formula. f(1) = -11 + 22(1-1) = -11 + 22(0) = -11 + 0 = -11.Determine Common Difference: Determine the common difference of the sequence. Since the coefficient of n in the explicit formula is 22, this indicates that the common difference, d, is 22. This is because each subsequent term increases by 22 from the previous term.Write Recursive Formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is given by: f(n) = f(n-1) + d, where d is the common difference. Since we have already determined that f(1) = -11 and d = 22, we can write the recursive formula as: f(n) = f(n-1) + 22.

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f(n)=-11+22(n-1)
Complete the recursive formula of
f(n).

{:[f(1)=◻],[f(n)=f(n-1)+]:}

$f(n)=-11+22(n-1)$ $\newline$ 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)=-11+22(n-1)

\newline

Complete the recursive formula of

f(n)

\newline

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

Identify First Term: Identify the first term of the sequence using the given explicit formula. The explicit formula is $f(n)=-11+22(n-1)$ . To find the first term, $f(1)$ , we substitute $n=1$ into the formula. $\newline$ $f(1) = -11 + 22(1-1) = -11 + 22(0) = -11 + 0 = -11$ .
Determine Common Difference: Determine the common difference of the sequence. Since the coefficient of $n$ in the explicit formula is $22$ , this indicates that the common difference, $d$ , is $22$ . This is because each subsequent term increases by $22$ from the previous term.
Write Recursive Formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is given by: $\newline$ $f(n) = f(n-1) + d$ , where $d$ is the common difference. $\newline$ Since we have already determined that $f(1) = -11$ and $d = 22$ , we can write the recursive formula as: $\newline$ $f(n) = f(n-1) + 22$ .