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I have no clue how to solve this, can someone help?

Given a positive sequence \(\{ a_n\} \) where \(a_1=2, a_2=5\), such that \(a_{n+1}^2=a_n \cdot a_{n+2}+3\) for all positive integers \(n\). Does there exist a constant \( b\) such that \(a_n+a_{n+2}=b \cdot a_{n+1}\) for any positive integer \(n\) ? Justify your answer.

Note by Sihfgrty Qhg
1 year, 5 months ago

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1 vote

  Easy Math Editor

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[example link](https://brilliant.org)example link
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    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

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# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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