{[f(1)=37],[f(n)=f(n-1)*0.3]:} Find an explicit formula for f(n). f(n)=

Given Sequence: We are given a recursive sequence where the first term is f(1) = 37 and each subsequent term is found by multiplying the previous term by 0.3. To find an explicit formula for f(n), we need to express f(n) in terms of n without referencing previous terms.Examining the Pattern: Let's examine the pattern of the sequence to find the explicit formula. We know that f(1) = 37. According to the recursive formula, f(2) would be f(1) * 0.3 = 37 * 0.3. Similarly, f(3) would be f(2) * 0.3 = (37 * 0.3) * 0.3. We can see that with each step, we are multiplying by an additional factor of 0.3.Generalizing the Pattern: To generalize this pattern, we can say that f(n) is equal to the first term, 37, multiplied by 0.3 raised to the power of (n-1), because for f(1), we have 0.3 raised to the power of 0 (which is 1), for f(2), we have 0.3 raised to the power of 1, and so on.Explicit Formula: Therefore, the explicit formula for f(n) is f(n) = 37 * (0.3)^(n-1).

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{[f(1)=37],[f(n)=f(n-1)*0.3]:}
Find an explicit formula for
f(n).

f(n)=

$\begin{cases} f(1)=37, f(n)=f(n-1)\times 0.3 \end{cases}$ 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)=37, f(n)=f(n-1)\times 0.3 \end{cases}

Find an explicit formula for

f(n)

f(n)=

Given Sequence: We are given a recursive sequence where the first term is $f(1) = 37$ and each subsequent term is found by multiplying the previous term by $0.3$ . To find an explicit formula for $f(n)$ , we need to express $f(n)$ in terms of $n$ without referencing previous terms.
Examining the Pattern: Let's examine the pattern of the sequence to find the explicit formula. We know that $f(1) = 37$ . According to the recursive formula, $f(2)$ would be $f(1) \times 0.3 = 37 \times 0.3$ . Similarly, $f(3)$ would be $f(2) \times 0.3 = (37 \times 0.3) \times 0.3$ . We can see that with each step, we are multiplying by an additional factor of $0.3$ .
Generalizing the Pattern: To generalize this pattern, we can say that $f(n)$ is equal to the first term, $37$ , multiplied by $0.3$ raised to the power of $(n-1)$ , because for $f(1)$ , we have $0.3$ raised to the power of $0$ (which is $1$ ), for $f(2)$ , we have $0.3$ raised to the power of $1$ , and so on.
Explicit Formula: Therefore, the explicit formula for $f(n)$ is $f(n) = 37 \cdot (0.3)^{(n-1)}$ .