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解
設等比數列〈〉的前n項和為S。已知S=5, Sq=20,求S的值。
2024.02.28 17:09

Answer 1

✨ 最佳解答 ✨

可知

由條件知
S2 = a1 + a2 = a1 + a1r = a1 • (1+r) = 5

S4 – S2 = a3 + a4 = a1 • r² (1+r) = 15

兩式相除可得
r² = 3，r = ±√3 代回得
① r=√3 時 a1 = (5/2)(√3–1)
S6 = (5/2)(√3–1) × (1–(√3)⁶)/(1–√3)
= (5/2)(√3–1) × 26/(√3–1)
= 65

② r=–√3 時 a1 = (–5/2)(√3+1)
S6 = (–5/2)(√3+1) × (1–(–√3)⁶)/(1–(–√3))
= (–5/2)(√3+1) × (–26)/(1+√3)
= 65

因此兩種情況算出來的S6 都是 65。