Recurrence equations - rekursjon
"}, "advice": "$y(2) = 2y(2-1)-y(2-2)=2y(1)-y(0) = 2 \\cdot 1 - 0 = 2$
\n$y(3) = 2y(3-1)-y_(3-2)=2y(2)-y(1) = 2 \\cdot 2 - 1 = 3$
\n$y(4) = 2y(4-1)-y(4-2)=2y(3)-y(2) = 2 \\cdot 3 - 2 = 4$
\nSo, it looks like $y_5=5, y_6=6,...$ and $y_n=n$.
", "parts": [{"prompt": "A sequence $y_n$ is defined by the recursive formula
\n$y_n = 2y_{n-1}-y_{n-2}$
\nwhere
\n$y(0)=0,\\;\\;y(1)=1$
\nFind the next 3 terms by using the recursion method.
\n$y(2)$ = [[0]] , $y(3)$ = [[1]] , $y(4)$ = [[2]]
\nCan you work out a direct formula for $y(n)$ = [[3]]
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\n$y_2 = 2y_{2-1}-y_{2-2}=2y_1-y_0 = 2 \\cdot 1 - 0 = 2$
\n$y_3 = 2y_{3-1}-y_{3-2}=2y_2-y_1 = ...$
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", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"prompt": "A sequence $y(n)$ is given by the recursive formula
\n$y(n) - 6y(n-1) +9y(n-2)= 2^n, \\;\\;y_0=1,\\;\\;y_1=2$
\nFind a direct formula for $y(n)$:
\n$y_n$ = [[0]]
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\n$y(n) - 3y(n-1) +2y(n-2)= 0, \\;\\;n\\geq3,\\;\\;y(1)=0,\\;\\;y(2)=2$
\nFind a direct formula for $y(n)$:
\n$y(n)$ = [[0]]
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\n$y(n) - 3y(n-1) = -4n, \\;y(0)=2$
\nFind a recurrence formula for $y(n)$:
\n$y(n)$ = [[0]]
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\nFind a recurrence formula for $y(n)$:
\n$y(n)$ = [[0]]
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