Найдите сумму первых 5 членов геометрической прогрессии:

1) b1=8, q=1/2 2) 3; - 6; ... 3) - 32; 16; ... 4) c1=-4; q=3 5) u1=3; q=2

1)

Sn=b₁ * (1-qⁿ) / (1-q)

b₁=8 q=1/2 n=5

S₅=8 * (1 - (1/2) ⁵) / (1-1/2) = 2³ * (1 - (1/2⁵) / (1/2) = (2³-2³/2⁵) * 2 = (2³-2⁻²) * 2=

=2⁴-2⁻¹=32-1/2=31,5.

2)

a₁=3 a₂=-6 ...

q=-6/3=-2

S₅=3 * (1 - (-2) ⁵) / (1 - (-2)) = 3 * (1+32) / 3==33.

3)

-32; 16; ... q=16 / (-32) = - 1/2

S₅ = (-32 * (1 - (-1/2) ⁵) / (1 - (-1/2)) = - 32 * (1+1/32) / (3/2) = - 32 * (1+1/32)) * 2/3=

=-4*33*2 / (32*3) = - 22.

4)

c₁=-4 q=3

S₅=4 * (1-3⁵) / (1-3) = - 4 * (1-243) / (-2) = - 4 * (-242) / (-2) = - 484.

5) u₁=3 q=2

S₅=3 * (1-2⁵) / (1-2) = 3 * (1-32) / (-1) = 3 * (-31) / (-1) = 93.