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Question Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 180,30,5, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \) Submit Answer

Ask by Hilton Lewis. in the United States
Mar 16,2025

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Answer

The explicit formula for \( a_n \) is: \[ a_n = 180 \cdot \left(\frac{1}{6}\right)^{n-1} \]

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Beyond the Answer

This sequence, \( 180, 30, 5, \ldots \), follows a pattern of division. Each term is divided by a decreasing factor: \( 180 \div 6 = 30 \), and \( 30 \div 6 = 5 \). Thus, the relationship can be captured as \( a_n = \frac{180}{6^{n-1}} \). This formula will generate the terms of the sequence as \( n \) increases! If you ever find sequences daunting, remember: they often have patterns hiding in plain sight! To find the \( n^{\text {th }} \) term, look for consistent operations like addition, subtraction, multiplication, or division. Keep an eye out for powers or other mathematical tricks that might reveal the secret formula!

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