Discrete Math 2.4.2 Recurrence Relations

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im having a hard time understanding why a2 + 3(n-2) actually makes sense. 10:23
the pattern was n-2, and i cant seem to understand how n-2 = a2.

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6:30

[@سبحانالله-ك2ذ]

Solve the recurrence relation:
𝑎𝑛 = 8𝑎𝑛−1 − 21𝑎𝑛−2 + 18𝑎𝑛−3, 𝑎0 = 5, 𝑎1 = 2, 𝑎2 = 13
?

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6:10