104學測數學考科-01

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<單選>每週同一時間點記錄某植物的成長高度,連續五週的數據為 \(a_1 = 1\), \(a_2 = 2\), \(a_3 = 6\), \(a_4 = 15\), \(a_5 = 31\)。請問此成長高度數列滿足下列選項中哪一個式子？
(1) \(a_{i+1} = 3a_i – 1\),\(i = 1, 2, 3, 4\)
(2) \(a_i = i!\),\(i = 1, 2, 3, 4, 5\)
(3) \(a_{i+1} = a_i + i^2\),\(i = 1, 2, 3, 4\)
(4) \(a_i = 2^i – 1\),\(i = 1, 2, 3, 4, 5\)
(5) \(a_{i+1} = i a_i + 1\),\(i = 1, 2, 3, 4\)