{[f(1)=-62],[f(n)=f(n-1)+5]:} Find an explicit formula for f(n). f(n)=

Identify sequence type: Identify the type of sequence described by the function f(n). Since f(n) is defined in terms of the previous term f(n-1) plus a constant, this indicates that the sequence is arithmetic.Determine first term and common difference: Determine the first term and the common difference of the sequence. The first term is given as f(1) = -62. The common difference is the amount added to each term to get the next term, which is 5.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence to express f(n). The explicit formula for an arithmetic sequence is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.Substitute values into formula: Substitute the values of a1 and d into the formula. Substituting the given values, we get f(n) = -62 + (n-1)×5.Simplify expression: Simplify the expression. Simplifying the expression, we get f(n) = -62 + 5n - 5, which further simplifies to f(n) = 5n - 67.

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{[f(1)=-62],[f(n)=f(n-1)+5]:}
Find an explicit formula for
f(n).

f(n)=

$\left\{\begin{array}{l} f(1)=-62 \\ f(n)=f(n-1)+5 \end{array}\right.$ $\newline$ 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)=-62 \\ f(n)=f(n-1)+5 \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 $f(n)$ . $\newline$ Since $f(n)$ is defined in terms of the previous term $f(n-1)$ plus a constant, this indicates that the sequence is arithmetic.
Determine first term and common difference: Determine the first term and the common difference of the sequence. $\newline$ The first term is given as $f(1) = -62$ . The common difference is the amount added to each term to get the next term, which is $5$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence to express $f(n)$ . $\newline$ The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$ , where $a_1$ is the first term and $d$ is the common difference.
Substitute values into formula: Substitute the values of $a_1$ and $d$ into the formula. $\newline$ Substituting the given values, we get $f(n) = -62 + (n-1)\times 5$ .
Simplify expression: Simplify the expression. $\newline$ Simplifying the expression, we get $f(n) = -62 + 5n - 5$ , which further simplifies to $f(n) = 5n - 67$ .