{[f(1)=-8],[f(n)=f(n-1)-3]:} 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) - 3 suggests that this is an arithmetic sequence because the difference between consecutive terms is constant.Determine first term: Determine the first term of the sequence. We are given that f(1) = -8, so the first term, a1, is -8.Find common difference: Determine the common difference of the sequence. The function f(n) = f(n-1) - 3 indicates that the common difference, d, is -3 because each term is 3 less 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 = -8 and d = -3.Write formula for sequence: Write the explicit formula for the sequence using the values from Step 4. The formula is f(n) = -8 + (n-1)(-3).Simplify the formula: Simplify the formula. f(n) = -8 - 3(n-1) = -8 - 3n + 3 = -3n - 5.

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{[f(1)=-8],[f(n)=f(n-1)-3]:}
Find an explicit formula for
f(n).

f(n)=

$\left\{\begin{array}{l} f(1)=-8 \\ f(n)=f(n-1)-3 \end{array}\right.$ $\newline$ 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)=-8 \\ f(n)=f(n-1)-3 \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 $f(n) = f(n-1) - 3$ suggests that this is an arithmetic sequence because the difference between consecutive terms is constant.
Determine first term: Determine the first term of the sequence. We are given that $f(1) = -8$ , so the first term, $a_1$ , is $-8$ .
Find common difference: Determine the common difference of the sequence. The function $f(n) = f(n-1) - 3$ indicates that the common difference, $d$ , is $-3$ because each term is $3$ less 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, $a_1 = -8$ and $d = -3$ .
Write formula for sequence: Write the explicit formula for the sequence using the values from Step $4$ . The formula is $f(n) = -8 + (n-1)(-3)$ .
Simplify the formula: Simplify the formula. $f(n) = -8 - 3(n-1) = -8 - 3n + 3 = -3n - 5$ .