document.write( "Question 1021209: The sequence u_n is defined recursively by the rules
\n" ); document.write( "u_1 = 3, u_2 = 3, u_(n+2) = u_(n+1) + 2u_n for all n ∈ N.
\n" ); document.write( "Find the formula for the general term of the sequence and prove it.
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Algebra.Com's Answer #637001 by richard1234(7193) $\"\"$ $\"About$

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The characteristic polynomial is

, which has roots

. So the general term is of the form

for some constants a and b.\r
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\n" ); document.write( "\n" ); document.write( "When n = 1, we have

.\r
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\n" ); document.write( "\n" ); document.write( "When n = 2, we have

\r
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\n" ); document.write( "\n" ); document.write( "Solving for a and b, we get a = 1, b = -1. So the general formula is\r
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for all

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