{[h(1)=-17],[h(n)=h(n-1)*0.2]:} Find an explicit formula for h(n). h(n)=

Given Information: We are given the first term of the sequence h(1) = -17 and a recursive formula h(n) = h(n-1) * 0.2. To find an explicit formula, we need to recognize the type of sequence we are dealing with.Identifying the Sequence Type: Since each term is obtained by multiplying the previous term by a constant factor (0.2), this sequence is geometric.Geometric Sequence Formula: For a geometric sequence, the nth term is given by the formula h(n) = a * r^(n-1), where a is the first term and r is the common ratio.Substituting Values: We already know the first term a = h(1) = -17 and the common ratio r = 0.2. Now we can substitute these values into the formula for the nth term of a geometric sequence.Final Explicit Formula: Substituting the values, we get h(n) = -17 * (0.2)^(n-1).

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{[h(1)=-17],[h(n)=h(n-1)*0.2]:}
Find an explicit formula for
h(n).

h(n)=

$\begin{cases} h(1)=-17, h(n)=h(n-1)\times 0.2 \end{cases}$ Find an explicit formula for $h(n)$ . $h(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

\begin{cases} h(1)=-17, h(n)=h(n-1)\times 0.2 \end{cases}

Find an explicit formula for

h(n)

h(n)=

Given Information: We are given the first term of the sequence $h(1) = -17$ and a recursive formula $h(n) = h(n-1) \times 0.2$ . To find an explicit formula, we need to recognize the type of sequence we are dealing with.
Identifying the Sequence Type: Since each term is obtained by multiplying the previous term by a constant factor $0.2$ ), this sequence is geometric.
Geometric Sequence Formula: For a geometric sequence, the nth term is given by the formula $h(n) = a \cdot r^{(n-1)}$ , where $a$ is the first term and $r$ is the common ratio.
Substituting Values: We already know the first term $a = h(1) = -17$ and the common ratio $r = 0.2$ . Now we can substitute these values into the formula for the $n$ th term of a geometric sequence.
Final Explicit Formula: Substituting the values, we get $h(n) = -17 \cdot (0.2)^{n-1}$ .