Question

kyuuuu

想請問高一下這題數學🙏🏻

Answer 1

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設 a₁ = a, 公比為 r
則 aₙ = arⁿ⁻¹

代入條件
{ ar - a = 2
{ a + ar² = 10

提出 a
{ a(r - 1) = 2
{ a(r² + 1) = 10

兩式相除
(r²+1)/(r-1) = 5

r² + 1 = 5(r - 1)
r² + 1 = 5r - 5
r² - 5r + 6 = 0
(r - 2)(r - 3) = 0
r = 2 或 3

a(r - 1) = 2
若 r = 2 則 a = 2
若 r = 3 則 a = 1

r = 2 的數列：2, 4, 8, 16, ...
r = 3 的數列：1, 3, 9, 27, ...

所以 a₄ = 16 或 27

kyuuuu

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