Геометриялық прогрессияның еселігін табу керек?

Question

Егер, b1=15, S3=21 бүтін 2/3. q?

Егер, b3=135, S3=195. q?

Answer 1

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

b1 , n=3

15 * (q^3 - 1) / (q-1) = 21 2/3

15*(q^3-1) / (q-1) = 65/3

q^2+q+1 = 65/45

q^2+q-4/9 = 0

D = 1+16/9 = 25/9

q = 1/3

[b_3=b_1\cdot q^2\\q=\sqrt{\cfrac{b_3}{b_1}}\\S_3=\cfrac{b_1(1-q^2)}{1-q}=b_1+b_1q\\b_1=\cfrac{b_3}{q^2}\\195=\cfrac{135}{q^2}+\cfrac{135}{q}\\q=\cfrac{12}{10}]

Answer 2

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

b1 , n=3

15 * (q^3 - 1) / (q-1) = 21 2/3

15*(q^3-1) / (q-1) = 65/3

q^2+q+1 = 65/45

q^2+q-4/9 = 0

D = 1+16/9 = 25/9

q = 1/3