{[h(1)=-26],[h(n)=h(n-1)*(-9)]:} Find an explicit formula for h(n). h(n)=

Given Information: We are given the first term of the sequence h(1) = -26 and a recursive formula h(n) = h(n-1) * (-9). To find an explicit formula for h(n), we need to recognize the pattern of the sequence.Recursive Formula: The sequence starts with h(1) = -26. Using the recursive formula, we can find the next few terms to identify the pattern: h(2) = h(1) * (-9) = -26 * (-9) = 234 h(3) = h(2) * (-9) = 234 * (-9) = -2106 We can see that each term is the previous term multiplied by -9.Identifying the Pattern: Since the sequence is formed by multiplying the previous term by -9, this is a geometric sequence with the first term a1 = -26 and common ratio r = -9.Geometric Sequence: The explicit formula for a geometric sequence is given by: a_n = a_1 * r^(n - 1) Substituting a_1 = -26 and r = -9 into the formula gives us: h(n) = -26 * (-9)^(n - 1)

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{[h(1)=-26],[h(n)=h(n-1)*(-9)]:}
Find an explicit formula for
h(n).

h(n)=

$\begin{cases} h(1)=-26, h(n)=h(n-1)\cdot(-9) \end{cases}$ $\newline$ Find an explicit formula for $h(n)$ . $\newline$ $\newline$ $h(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

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\begin{cases} h(1)=-26, h(n)=h(n-1)\cdot(-9) \end{cases}

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Find an explicit formula for

h(n)

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h(n)=

Given Information: We are given the first term of the sequence $h(1) = -26$ and a recursive formula $h(n) = h(n-1) \times (-9)$ . To find an explicit formula for $h(n)$ , we need to recognize the pattern of the sequence.
Recursive Formula: The sequence starts with $h(1) = -26$ . Using the recursive formula, we can find the next few terms to identify the pattern: $\newline$ $h(2) = h(1) \cdot (-9) = -26 \cdot (-9) = 234$ $\newline$ $h(3) = h(2) \cdot (-9) = 234 \cdot (-9) = -2106$ $\newline$ We can see that each term is the previous term multiplied by $-9$ .
Identifying the Pattern: Since the sequence is formed by multiplying the previous term by $-9$ , this is a geometric sequence with the first term $a_1 = -26$ and common ratio $r = -9$ .
Geometric Sequence: The explicit formula for a geometric sequence is given by: $\newline$ $a_n = a_1 \cdot r^{(n - 1)}$ $\newline$ Substituting $a_1 = -26$ and $r = -9$ into the formula gives us: $\newline$ $h(n) = -26 \cdot (-9)^{(n - 1)}$