Question

Majac dane pierwsze dwa wyrazy ciagu geometrycxnego, wyznacz trzy kolejne (prosze z obliczeniami). A) 2,6,... B) 5pierw.z5, 5,... C) 4, -2,... D) -27/16, -9/8,... /- to kreska ulamkowa

Answer 1

A) q=6/2=3
a₃ = a₁ * q² = 2 *3²=2*9=18
a₄ = a₁* q³ = 2*27 =54
a₅ = a₁ * q⁴ = 2*81=162
an= (2,6,18,54,162)
b) q=5/5√5 = 1/√5
a₃ = a₁*q² = 5√5 * 1/5 = √5
a₄ = a₁ * q³ = 5√5 * 1/5√5 = 1
a₅ = a₁*q⁴ = 5√5 * 1/25 = √5/5
an = (5√5, 5, √5, 1 , √5/5)
c) q = -2/4 = -1/2
a3 = a₁*q² = 4* 1/4 = 1
a4 = a₁ * q³ = 4* (-1/8) = -1/2
a5 = a₁*q⁴  = 4 * 1/16 = 1/4
an = (4,-2, 1 , -1/2, 1/4)
d) q = -9/8/-27/16= -9/8*(-16/27)=2/3
a3 = a₁*q² = -27/16 * 4/9 = -3/4
a4 = a₁ * q³ = -27/16 * 8/27 = -1/2
a5 = a₁*q⁴   = -27/16 * 16/81= -1/3
an = (-27/16, -9/8, -3/4, -1/2, -1/3)