Question

100 баллов
геометрическая прогрессии ​

Answer 1

bn = b1 * q^(n-1) n-й член прогрессии

Sn = b1*(q^n - 1)/(q - 1) сумма n членов

5

b4 - b2 = 24

b2 + b3 = 6

сложим

b4 - b2 + b3 + b2 = 24 + 6

b3 + b4 = 30

b2 + b3 = 6

b1*q^2 + b1*q^3 = q*(b1*q + b1*q^2) = 30 (1)

b1*q + b1*q^2 = 6 (2)

делим (1) на (2)

q*(b1*q + b1*q^2)/(b1*q + b1*q^2) = q = 5

5*b1 + 25*b1 = 6 подставляем в (2)

30 b1 = 6

b1 = 1/5

b4 = b1*q^3 = 1/5 * (5^3) = 25

6

S3 = 39    b1 = 27

S3 = b1*(q^3 - 1)/(q - 1) = b1*(q - 1)(q^2 + q + 1)/(q-1) = b1(q^2 + q + 1)

39 = 27(q^2 + q + 1)

27q^2 + 27q - 12 = 0

9q^2 + 9q - 4 = 0

D = 9^2 - 4*(-4)*9 = 81 + 144 = 225 = 15^2

b12=(-9+-15)/18 = 1/3    -4/3

b1=1/3

b2 = -4/3