b₁ = b₁

b₂ = b₁q

b₃ = b₁q²

b₄ = b₁q³

b₁ + b₁q³ = 14

b₁q + b₁q² = 6

--

b₁(1 + q³) = 14

b₁q(1 + q) = 6

делим

(1 + q³)/q(1 + q) = 14/6

6(1 - q + q²) = 14q

3 - 3q + 3q² - 7q = 0

3q² - 10q + 3 = 0

D = 100 - 36 = 64

q₁₂ = (10 +- 8)/6 = 3    1/3

1/3 - нет, прогрессия убывающая

q = 3

b₁q(1 + q) = 6

b₁ *3(1 + 3) = 6

b₁ = 1/2

b₂ = 1/2 * 3 = 3/2

b₃ = 3/2 * 3 = 9/2

b₄ = 9/2 * 3 = 27/2

ответ b₄  = 27/2