$\\begin{cases} h(1) = -26 \\\\ h(n) = h(n - 1) \\cdot (-9) \\end{cases}$\nfind an explicit formula for…
$\\begin{cases} h(1) = -26 \\\\ h(n) = h(n - 1) \\cdot (-9) \\end{cases}$\nfind an explicit formula for $h(n)$.\n$h(n) = \\square$
Answer
Explanation:
Step1: Identify sequence type
This is a geometric sequence, where each term is the previous term multiplied by a common ratio $r=-9$, with first term $h(1)=-26$.
Step2: Recall geometric sequence formula
The explicit formula for a geometric sequence starting at $n=1$ is $h(n) = h(1) \cdot r^{n-1}$.
Step3: Substitute known values
Substitute $h(1)=-26$ and $r=-9$ into the formula: $h(n) = -26 \cdot (-9)^{n-1}$
Answer:
$h(n) = -26 \cdot (-9)^{n-1}$