решить геометрическую прогрессию в6+в7=60 в5+в6=15 Найти в8
Решаем систему:
в6+в7=60
в5+в6=15
b1q^5+b1q^6=60
b1q^4+b1q^5=15
b1q^5(1+q)=60
b1q^4(1+q)=15
1+q=60/(b1q^5)
1+q=15/(b1q^4)
60/(b1q^5)=15/(b1q^4)
4/q=1
q=4
b1*(4^4)(1+4)=15
b1*(4^4)*5=15
b1*(4^4)=3
b1=3/(4^4)
b8=b1q^7=(3/(4^4))*(4^7)=3*(4^3)=3*64=192
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Verified answer
Решаем систему:
в6+в7=60
в5+в6=15
b1q^5+b1q^6=60
b1q^4+b1q^5=15
b1q^5(1+q)=60
b1q^4(1+q)=15
1+q=60/(b1q^5)
1+q=15/(b1q^4)
60/(b1q^5)=15/(b1q^4)
4/q=1
q=4
b1*(4^4)(1+4)=15
b1*(4^4)*5=15
b1*(4^4)=3
b1=3/(4^4)
b8=b1q^7=(3/(4^4))*(4^7)=3*(4^3)=3*64=192