Complete the recursive formula of the geometric sequence
$$
\begin{array}{l}
-1.5,6,-24,96, \ldots . \
d(1)=\square \
d(n)=d(n-1) .
\end{array}
$$

Question

Complete the recursive formula of the geometric sequence
$$
\begin{array}{l}
-1.5,6,-24,96, \ldots . \
d(1)=\square \
d(n)=d(n-1) .
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the first term of the geometric sequence. ‖ ‖ step 2 ⋮ The first term of the sequence is $-1.5$, so $d(1) = -1.5$. ‖ ‖ step 3 ⋮ Determine the common ratio by dividing the second term by the first term. ‖ ‖ step 4 ⋮ The common ratio $r$ is $\frac{6}{-1.5} = -4$. ‖ ‖ step 5 ⋮ Write the recursive formula using the first term and the common ratio. ‖ ‖ step 6 ⋮ The recursive formula is $d(n) = d(n-1) \cdot r$. ‖ ‖ step 7 ⋮ Substitute the common ratio $-4$ into the recursive formula. ‖ ‖ step 8 ⋮ The complete recursive formula is $d(n) = d(n-1) \cdot (-4)$. ‖ ∻Answer∻ ⚹ $d(1) = -1.5$, $d(n) = d(n-1) \cdot (-4)$ for $n > 1$ ⚹ ∻Key Concept∻ ⚹Geometric Sequence Recursive Formula⚹ ∻Explanation∻ ⚹The recursive formula for a geometric sequence is defined by the first term and the common ratio, which is the factor by which each term is multiplied to obtain the subsequent term.⚹◊What is the common ratio (r) of the geometric sequence given (-1.5, 6, -24, 96, ...)?⍭ Generate me a similar question◊

Sia