{[f(1)=-1.8],[f(n)=f(n-1)*9]:} Find an explicit formula for f(n). f(n)=

Given sequence and terms: We are given a recursive sequence where the first term f(1) is -1.8 and each subsequent term is obtained by multiplying the previous term by 9. To find an explicit formula, we need to express f(n) in terms of n without referring to f(n-1).Identifying the pattern: Let's look at the first few terms to identify a pattern: f(1) = -1.8 f(2) = f(1) * 9 = -1.8 * 9 f(3) = f(2) * 9 = (-1.8 * 9) * 9 We can see that each term is the first term multiplied by 9 raised to the power of (n-1).Geometric sequence formula: The explicit formula for a geometric sequence is given by: f(n) = a * r^(n - 1) where a is the first term and r is the common ratio. In this case, a = f(1) = -1.8 and r = 9.Substituting values into the formula: Substitute the values of a and r into the formula to get the explicit formula for f(n): f(n) = -1.8 * 9^(n - 1) This is the explicit formula for the given recursive sequence.

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{[f(1)=-1.8],[f(n)=f(n-1)*9]:}
Find an explicit formula for
f(n).

f(n)=

$\begin{cases} f(1)=-1.8, f(n)=f(n-1)\times 9 \end{cases}$ Find an explicit formula for $f(n)$ . $f(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

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\begin{cases} f(1)=-1.8, f(n)=f(n-1)\times 9 \end{cases}

Find an explicit formula for

f(n)

f(n)=

Given sequence and terms: We are given a recursive sequence where the first term $f(1)$ is $-1.8$ and each subsequent term is obtained by multiplying the previous term by $9$ . To find an explicit formula, we need to express $f(n)$ in terms of $n$ without referring to $f(n-1)$ .
Identifying the pattern: Let's look at the first few terms to identify a pattern: $\newline$ $f(1) = -1.8$ $\newline$ $f(2) = f(1) \times 9 = -1.8 \times 9$ $\newline$ $f(3) = f(2) \times 9 = (-1.8 \times 9) \times 9$ $\newline$ We can see that each term is the first term multiplied by $9$ raised to the power of $(n-1)$ .
Geometric sequence formula: The explicit formula for a geometric sequence is given by: $\newline$ $f(n) = a \cdot r^{(n - 1)}$ $\newline$ where $a$ is the first term and $r$ is the common ratio. In this case, $a = f(1) = -1.8$ and $r = 9$ .
Substituting values into the formula: Substitute the values of $a$ and $r$ into the formula to get the explicit formula for $f(n)$ : $f(n) = -1.8 \times 9^{(n - 1)}$ This is the explicit formula for the given recursive sequence.