It is known that an = 2A (n-1) + 2 ^ n-1 (n ≥ 2) A1 = 5, A2 = 13, A3 = 33, A4 = 81. {(an + α) / 2 ^ n} is an arithmetic sequence, and a is obtained

It is known that an = 2A (n-1) + 2 ^ n-1 (n ≥ 2) A1 = 5, A2 = 13, A3 = 33, A4 = 81. {(an + α) / 2 ^ n} is an arithmetic sequence, and a is obtained


An = 2A (n-1) + 2 ^ n-1 divide both sides of the equation by 2 ^ n to get an / 2 ^ n = a (n-1) / 2 ^ (n-1) - 1 / 2 ^ n + 1 ① {(an + α) / 2 ^ n} is an arithmetic sequence, so (an + α) / 2 ^ n = (a (n-1) + α) / 2 ^ (n-1) + D (D is a parameter) is sorted out as an / 2 ^ n = a (n-1) + α / 2 ^ n + D ② Yes

Elden Ring Premiere

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