1) г. п

b1+b2+b3=26

b1*b2*b3=216

S5=?

2) а. п

a1+a2+a3=96

a2=4a1

a1=?

1)

b₁+b₂+b₃=26 b₁+b₁q+b₁q²=26 b₁ * (1+q+q²) = 26

b₁*b₂*b₃=216 b₁*b₁q*b₁q²=216 b₁³*q³=216 (b₁q) ³=6³ b₁q=6 b₁=6/q

(6/q) * (1+q+q²) = 26

6 * (1+q+q²) = 26q |:2

3+3q+3q²=13q

3q²-10q+3=0 D=64

q₁=3 ⇒ b₁=6/3=2 S₅=2 * (3⁵-1) / (3-1) = 2*242/2=242.

q₂=1/3 ⇒ b₁=6 / (1/3) = 18 S₅=18+6+2+2/3+2/9=26⁸/₉.

2)

a₁+a₂+a₃=96 a₁+a₁+d+a₁+2d=96 3a₁+3d=96 d+3d=96 4d=96 d=24

a₂=4a₁ a₁+d=4*a₁ 3a₁=d a₁=d/3 a₁=24/3 a₁=8.