Question

Math

Posted 3 months ago

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

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Answer from Sia

Posted 3 months ago

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.

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