Resposta :
Resposta:Segue as contas abaixo na explicação
Explicação passo a passo:
1)a6=300,q=2,n=6,a1=?
an=a1.q^n-1
300=2^6-1.a1
300=2^5.a1
300=32.a1
a1=300/32:4/4
a1=75/8
2)a5=100,n=5,a1=5,q=?
an=a1.q^n-1
100=5.q^5-1.
100=5.q^4
q^4=100/5
q^4=20
q= ± 4^√20
PG(5,5.4^√20,10.5^1/2,10.4^√20.5^1/2,100)
PG(5,-5.4^√20,10.5^1/2,-10.4^√20.5^1/2,100)
3)a1=7,an=5103,n=3,n=?
an=a1.q^n-1
5103=7.3^n-1
5103/7=3^n-1
729=3^n-1
3^6=3^n-1
6=n-1
n=6+1
n=7
4)a1=10,q=a2/a1--->q=20/10--->2,n=10,a10=?
an=a1.q^n-1
a10=10.2^10-1
a10=10.2^9
a10=10.512
a10=5120
5)a1=1/4,q=a2/a1--->1/4/1/4--->q=1,n=15,S15=?
Sn=a1.[(q^n)-1]/q-1
S15=1/4.[(1^15)-1]/1-1
S15=1/4.[1-1]/0
S15=1/4.0/0
S15=0