17. Вычислите сумму первых девяти членов геометрической прогрессии, если: a) C₁ = -4, q = 3; B) C₁ = -2, q = 2; б) с₁ = 1, q = -2; г) с₁ = 32, q = -0,5.

a) C₁ = -4, q = 3

\[ S_9 = \frac{-4 \cdot (1 - 3^9)}{1 - 3} = \frac{-4 \cdot (1 - 19683)}{-2} = 2 \cdot (-19682) = -39364 \]

б) с₁ = 1, q = -2

\[ S_9 = \frac{1 \cdot (1 - (-2)^9)}{1 - (-2)} = \frac{1 - (-512)}{3} = \frac{513}{3} = 171 \]

в) C₁ = -2, q = 2

\[ S_9 = \frac{-2 \cdot (1 - 2^9)}{1 - 2} = \frac{-2 \cdot (1 - 512)}{-1} = -2 \cdot (-511) = 1022 \]

г) с₁ = 32, q = -0,5

\[ S_9 = \frac{32 \cdot (1 - (-0.5)^9)}{1 - (-0.5)} = \frac{32 \cdot (1 - (-\frac{1}{512}))}{1.5} = \frac{32 \cdot (1 + \frac{1}{512})}{1.5} = \frac{32 \cdot \frac{513}{512}}{1.5} = \frac{32 \cdot 513}{512 \cdot 1.5} = \frac{16416}{768} = 21.375 \]