Calcule as progressões!!!
Soluções para a tarefa
Resposta:Segue as contas abaixo na explicação
Explicação passo-a-passo:
1)a2=8,a5=512,q=?,a1=?
an=ak.q^n-k an=a1.q^n-1
512=8.q^5-2 512=4^5-1.a1
512=8.q^3 512=4^4.a1
q^3=512/8 512=64.a1
q^3=64 a1=512/64
q=3^√64 a1=8
q=3^√4^3
q=4
PG(8,32,128,512)
2)a1=1/4,a7=16,n=7,q=?
an=a1.q^n-1
16=1/4.q^7-1
16=1/4.q^6
q^6=64
q= ± 6√64
q= ± 6√2^6
q= ± 2
3)a3=1/81,a7=81,q=?,a1=?
an=ak.q^n-k
81=1/81.q^7-3
81=1/81.q^4
q^4=6561
q= ± 4√6561
q= ± 4√9^4
q= ± 9
4)a9=1280,n=9,q=2,a1=?
an=a1.q^n-1
1280=2^9-1.a1
1280=2^8.a1
1280=128.a1
a1=1280/128
a1=10
5)K=4--->n=K+2--->n=4+2--->n=6,a1=1,a6=243,q=?
an=a1.q^n-1
243=1.q^6-1
243=1.a^5
q^5=243
q=5^√243
q=5^√3^5
q=3
6)a1=256,q=a2/a1--->q=128/256:128/128--->q=1/2--->q=0,5,Sn=480 m,
Sn=a1.[(q^n)-1]q-1
480=256.[(1/2^n)-1]/1/2-1
480=256.[(1/2^n)-1]/1/2-2/2
480=256.[(1/2^n)-1/-1/2
480=256.[(2^-n)-1].(-2)
480=-512.[(2^-n)-1]
480/-512=(2^-n)-1
-15/16=(2^-n)-1
-15/16+1=(2^-n)-1+1
-15/16+16/16=2^-n
-1/16=2^-n
1/2^4=2^-n
2^-4=2^-n
-4=-n(-1)
n=4