Общий член bn=b1*qⁿ⁻¹
b5=b1*q⁴=-1/4
b10=b1*q⁹=8
делим b10/b5=q⁵
q⁵=-8/(1/4)=-32 q=-2 b1=-(1/4)/(-32)=1/8
b15=1/8*(-2)¹⁴=2048
Решение
2^[(3x + 9) / (3x - 1)] = 64
2^[(3x + 9) / (3x - 1)] = 2⁶
(3x + 9) / (3x - 1) = 6
[(3x + 9) - 6*(3x - 1)] / (3x - 1) = 0
(3x + 9) - 6*(3x - 1) = 0
3x - 1 ≠ 0, x ≠ 1/3
3x + 9 - 18x + 6 = 0
- 15x = - 15
x = 1
Xn = q^(n-1) X1, q > 1 (при X1 > 0)
(X5 - X1) = 5(X3 - X1)
(q^4 - 1)X1 = 5(q^2 - 1)X1
(q^2 + 1)(q^2 - 1) = 5(q^2 - 1)
(q^2 - 4)(q^2 - 1) = 0
(q + 2)(q - 2)(q + 1)(q - 1) = 0
q > 1 --> q = 2