{[f(1)=72],[f(n)=f(n-1)+9]:} Find an explicit formula for f(n). f(n)=

Identify Sequence Type: Identify the type of sequence described by the function f(n). The function f(n) = f(n-1) + 9 suggests that this is an arithmetic sequence because there is a constant difference between consecutive terms.Determine First Term: Determine the first term of the sequence. We are given that f(1) = 72, which means the first term, a1, is 72.Find Common Difference: Determine the common difference of the sequence. The function f(n) = f(n-1) + 9 indicates that the common difference, d, is 9 because each term is 9 more than the previous term.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, which is an = a1 + (n-1)d. Substitute the values of a1 and d into the formula. In this case, a1 = 72 and d = 9.Write Formula: Write the explicit formula for the sequence using the values from Step 2 and Step 3. The formula is f(n) = 72 + (n-1)×9.Simplify Formula: Simplify the formula. Multiply 9 by (n-1) to get 9n - 9. Add this to the first term, 72, to get f(n) = 72 + 9n - 9.Combine Like Terms: Combine like terms to get the final explicit formula. f(n) = 9n + 72 - 9 simplifies to f(n) = 9n + 63.

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{[f(1)=72],[f(n)=f(n-1)+9]:}
Find an explicit formula for
f(n).

f(n)=

$\left\{\begin{array}{l} f(1)=72 \\ f(n)=f(n-1)+9 \end{array}\right.$ $\newline$ Find an explicit formula for $f(n)$ . $\newline$ $f(n)=$

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Algebra 2

Write a formula for an arithmetic sequence

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\left\{\begin{array}{l} f(1)=72 \\ f(n)=f(n-1)+9 \end{array}\right.

\newline

Find an explicit formula for

f(n)

\newline

f(n)=

Identify Sequence Type: Identify the type of sequence described by the function $f(n)$ . The function $f(n) = f(n-1) + 9$ suggests that this is an arithmetic sequence because there is a constant difference between consecutive terms.
Determine First Term: Determine the first term of the sequence. We are given that $f(1) = 72$ , which means the first term, $a_1$ , is $72$ .
Find Common Difference: Determine the common difference of the sequence. The function $f(n) = f(n-1) + 9$ indicates that the common difference, $d$ , is $9$ because each term is $9$ more than the previous term.
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, which is $a_n = a_1 + (n-1)d$ . Substitute the values of $a_1$ and $d$ into the formula. In this case, $a_1 = 72$ and $d = 9$ .
Write Formula: Write the explicit formula for the sequence using the values from Step $2$ and Step $3$ . The formula is $f(n) = 72 + (n-1)\times9$ .
Simplify Formula: Simplify the formula. Multiply $9$ by $(n-1)$ to get $9n - 9$ . Add this to the first term, $72$ , to get $f(n) = 72 + 9n - 9$ .
Combine Like Terms: Combine like terms to get the final explicit formula. $f(n) = 9n + 72 - 9$ simplifies to $f(n) = 9n + 63$ .