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Illustration depicting a sequence: 1, 2, 6, 14, 30, with an arrow showing the pattern of addition and doubling to reach each subsequent term

Ask AI: The first term is 1 and the second term 2. The rest of the terms are found by adding the two terms before it together, and then doubling the answer.

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Question: The first term is 1 and the second term 2. The rest of the terms are found by adding the two terms before it together, and then doubling the answer.

Asked by tumi

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It sounds like you're trying to describe a sequence where each term (starting from the third term) is found by adding the two previous terms and then doubling the result. Let's define this sequence step by step. 1. The first term (\(a_1\)) is 1. 2. The second term (\(a_2\)) is 2. 3. For \(n \geq 3\), the \(n\)-th term (\(a_n\)) is found by the formula: \[ a_n = 2 \times (a_{n-1} + a_{n-2}) \] Let's compute a few terms of this sequence to understand the pattern: 1. \( a_1 = 1 \) 2. \( a_2 = 2 \) 3. \( a_3 = 2 \times (a_2 + a_1) = 2 \times (2 + 1) = 2 \times 3 = 6 \) 4. \( a_4 = 2 \times (a_3 + a_2) = 2 \times (6 + 2) = 2 \times 8 = 16 \) 5. \( a_5 = 2 \times (a_4 + a_3) = 2 \times (16 + 6) = 2 \times 22 = 44 \) 6. \( a_6 = 2 \times (a_5 + a_4) = 2 \times (44 + 16) = 2 \times 60 = 120 \) So the first six terms of the sequence are: 1, 2, 6, 16, 44, 120. If you need more terms or further assistance with this sequence, feel free to ask!

Answered by gpt-4o

May 19, 2024, 9:38 a.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user tumi's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Sunday, May 19, 2024

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