{[f(1)=-71],[f(n)=f(n-1)*4.2]:} Find an explicit formula for f(n). f(n)=

Given information: We are given that f(1) = -71 and that f(n) is 4.2 times f(n-1). To find an explicit formula for f(n), we need to express f(n) in terms of n without the recursion.Identifying sequence type: Since f(n) = f(n-1) * 4.2, we can see that each term is 4.2 times the previous term. This is a geometric sequence with the first term f(1) = -71 and the common ratio r = 4.2.Geometric sequence formula: The explicit formula for the nth term of a geometric sequence is given by f(n) = a * r^(n-1), where a is the first term and r is the common ratio.Substitute values: Substitute a = -71 and r = 4.2 into the formula to get f(n) = -71 * 4.2^(n-1).

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{[f(1)=-71],[f(n)=f(n-1)*4.2]:}
Find an explicit formula for
f(n).

f(n)=

$\begin{cases} f(1)=-71, f(n)=f(n-1)\times 4.2 \end{cases}$ Find an explicit formula for $f(n)$ . $f(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

\begin{cases} f(1)=-71, f(n)=f(n-1)\times 4.2 \end{cases}

Find an explicit formula for

f(n)

f(n)=

Given information: We are given that $f(1) = -71$ and that $f(n)$ is $4.2$ times $f(n-1)$ . To find an explicit formula for $f(n)$ , we need to express $f(n)$ in terms of $n$ without the recursion.
Identifying sequence type: Since $f(n) = f(n-1) \times 4.2$ , we can see that each term is $4.2$ times the previous term. This is a geometric sequence with the first term $f(1) = -71$ and the common ratio $r = 4.2$ .
Geometric sequence formula: The explicit formula for the $n$ th term of a geometric sequence is given by $f(n) = a \cdot r^{(n-1)}$ , where $a$ is the first term and $r$ is the common ratio.
Substitute values: Substitute $a = -71$ and $r = 4.2$ into the formula to get $f(n) = -71 \times 4.2^{(n-1)}$ .