1.
d = -1/6 : (-1/3) = 1/2
-1/3 * (1/2 )⁵ = 3/6 = - 1/3* 1/32 = - 1/96
ОТвет: 3
2.
b₆ = b₁*q⁵ = 32
b₃ = b₁*q² = 4
32:4 = q⁵⁻² = q³ = 8
q = 2
b₁ = 4:q² = 4:4 = 1
Ответ: 1
3.
b₄ = b₁*q³
q³ = b₄ : b₁ = 8 : 1 = 8 = 2³
q = 2
S = b₁(qⁿ - 1)/(q-1)
S = 1(2⁶ -1)/(2-1) = 2⁶ - 1 = 63
Ответ: 3
4.
b₇ = b₁*q⁶
b₃ = b₁*q²
b₇/b₃ = q⁶/q² = q⁶⁻² = q⁴
1/32 : 1/2 = 1/16
q⁴ = 1/16
q = 1/2
Ответ: 1/2
5.
b₆ - b₄ = 144 b₁q²(q³ - q) = 144
b₅ - b₃ = 48 b₁q²(q² - 1) = 48
(q³- q)/(q²-1) = 144/48
q(q²-1)/(q²-1) = 3
q = 3
b₁ = 48/(q²(q²-1))
b₁ = 48/(9*8) = 48/72 = 2/3
Ответ: 2/3 и 3