S18/S9=7

S18=b1(q^18-1)/q-1

S9=b1(q^9-1)/q-1

b1(q^18-1)/q-1/ b1(q^9-1)/q-1=7

q^18-1/q^9-1=7

q^18-1=7q^9-7

q^9+1=7

q^9=6

q=6^(1/9)

(b1(6^2-1)/(6^(1/9)-1))/(b1(6-1)/(6^(1/9)-1)=7

35b1/7b1=7

5b1=7

b1=7/5

то есть  b1=7/5

 q=6^(1/9)

 (b43-b15)=b1(q^42-q^14)=7/5(6^(42/9)-6^(14/9))

 (b34-b6)=b1(q^33-q^5) =7/5(6^(33/9)-6^(5/9))=6

Ответ  6

Verified answer

(b43-b15)/(b34-b6) = (b1q^42-b1q^14)/(b1q^33-b1q^5) = (q^42-q^14)/(q^33-q^5) = q^14(q^28-1)/q^5(q^28-1)=q^14/q^5=q^9

S18/S9=7
b1(q^18-1)/(q-1) * (q-1)/b1(q^9-1)=7
(q^18-1)/(q^9-1)=7
 (q^9-1)(q^9+1)/(q^9-1)=7
q^9+1=7
q^9=6

Ответ: 6