1.
а₅ = 61
а₁₁ = 1647
а₂ - ?
Решение.
1)
а₅ = а₁·q⁴ => a₁·q⁴ = 61 => a₁ = 61/q⁴
2)
a₁₁ = a₁·q¹⁰ => a₁·q¹⁰ = 1647 => a₁ = 1647/q¹⁰
3)
61/q⁴ = 1647/q¹⁰
61q¹⁰ = 1647q⁴
61 q⁶ = 1647
q⁶ = 1647 : 61
q⁶ = 27
q⁶ = 3³
q = √3
4)
a₁ = 61/q⁴
a₁ = 61/(√3)⁴ = 61/9
5)
a₂=a₁*q
a₂= 61/9 *√3= 61√3/9
a₂= 61√3/9
2.
a₇=62500
q=5
a₁ - ?
a₇ = a₁·q⁶ => a₁ = a₇/q⁶
q⁶ = 5⁶ = 5⁴ · 5² = 625 · 25
q⁶ = (625·25)
a₁ = 62500/(625·25) = 100/25 = 4
a₁ = 4