QuestionFind the recursive formula for the sequence $2, -10, 50, -250, \ldots$ . Options: A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. The given sequence is a geometric sequence. . The sequence is $,-10,50,-250, \ldots$
3. We need to find the recursive formula for this sequence.

STEP 2

A recursive formula for a geometric sequence has the form $\left\{\begin{array}{l}a_{1}=first\, term \\ a_{n}=a_{n-1} \cdot common\, ratio\end{array}\right.$

STEP 3

From the given sequence, we can see that the first term, $a1$ , is $2$ .

STEP 4

To find the common ratio, we divide the second term by the first term, the third term by the second term, and so on. $Common\, ratio = \frac{a_{n}}{a_{n-1}}$

STEP 5

Calculate the common ratio using the first and second terms of the sequence.
$Common\, ratio = \frac{-10}{2} = -5$

STEP 6

Now that we have the first term and the common ratio, we can write the recursive formula for the sequence.
$\left\{\begin{array}{l}a_{1}=2 \\ a_{n}=a_{n-1} \cdot (-5)\end{array}\right.$
So, the answer is option A.

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