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  "body": "\n## Summary\n\nAn initial value problem for a recurrence asks for a sequence that satisfies a given recurrence and has prescribed first terms.\nFor a recurrence of order $k$ in explicit form, prescribing $k$ initial values gives exactly one solution.\nIt is the discrete counterpart of the [[initial value problem|0FXDW992DS]] for ordinary differential equations.\n\n## Explanations\n\n### L1 human\n\nA recurrence is a rule that builds each term of a sequence from the terms before it.\nThe rule alone does not tell you where to start.\nAn initial value problem fixes the starting terms, and then the rule produces everything else.\nFor example, $u_{n+1} = 2u_n$ with $u_0 = 3$ gives $3, 6, 12, 24, \\dots$, that is $u_n = 3 \\cdot 2^n$.\n",
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