QQuestionMathematics
QuestionMathematics
What is the recursive formula for this geometric sequence? $- 4,- 24,- 144,- 864, \ldots$
O A. $\left\{\begin{array}{l}a_{1}=- 4 \\ a_{n}=a_{n- 1} \bullet 6\end{array}\right.$
O B. $\left\{\begin{array}{l}a_{1}=- 6 \\ a_{n}=a_{n- 1} \bullet 30\end{array}\right.$
O C. $\left\{\begin{array}{l}a_{1}=- 4 \\ a_{n}=a_{n- 1} \bullet 30\end{array}\right.$
O D. $\left\{\begin{array}{l}a_{1}=- 6 \\ a_{n}=a_{n- 1} \bullet 4\end{array}\right.$
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Identify the first term and the common ratio
\frac{-864}{-144} = 6
- Let's find the common ratio by dividing consecutive terms:
Step 3:: Verify the pattern
- Fourth term: $$-144 \times 6 = -864
- Second term: - 4 \times 6 = - 24
Step 4:: Construct the recursive formula
- First term: $$a_{1} = -4
- Recursive rule: a_{n} = a_{n- 1} \times 6
Step 5:: Match with given options
- This matches option A: $$\left\{\begin{array}{l}a_{1}=-4 \ a_{n}=a_{n-1} \bullet 6\end{array}\right.
Final Answer
Option A is the correct recursive formula for this geometric sequence.
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