Odpowiedź:
12,135
a)
an = - 4 * (- 1)ⁿ
a₁ =- 4 * (- 1)¹ = - 4 * (- 1) = 4
b)
an= (1/3)ⁿ⁻¹
a₁= (1/3)¹⁻¹ = (1/3)⁰ = 1
c)
an= 2⁻ⁿ
a₁= 2⁻¹ = 1/2
12.136
a(k)/a(m)= q^(k - m)
a)
a₅=1/81
a₉ = 1/64
a₅/a₉ = q⁵⁻⁹ = q⁻⁴ = (1/q)⁴
(1/q)⁴= 1/81 : 1/64 = 1/81 * 64 = 64/81
(1/q) = ⁴√(64/81)
q = 1/⁴√(64/81) = ⁴√(4/3): 64/81 = ⁴√(4/3)/⁴√(256/243 = ⁴√(4/3) : 4/3 =
= ⁴√(4/3)* 3/4 = 3⁴√(4/3)/4
b)
a₃= - 8
a₆ = - 125
a₃/a₆=q³⁻⁶ = q⁻³
- 8/(- 125) = q⁻³ = 1/q
(1/q)³ = 8/125
1/q = ∛(8/125) = 2/5
q = 5/2 = 2,5
12.138
b)
a₁ = 10
a₂ = a₁q = 10²
a₁q/a₁ = q
q = 10²/10 = 10
a₁₀ = 10¹⁰
s₁₀ = a₁(1 - q¹⁰)/(1 - q) = 10(1 - 10¹⁰)/(1 - 10) = (10 - 10¹¹)/(- 9) =
= (10 - 100000000000)/(- 9) = - 99999999990/(- 9) =
= 9999999990/9 = 11111111110
