Question

Calcule a soma dos infinitos termos das P.G’s. seguintes.

a) (48, 12, 3, ... ) b) (75, 15, 3, ... )

c) (–98, 14, –2, ... ) d) (175, –35, 7, ... )

e) (–80, –20, –5, ... ) f) (–648, –72, –8, ... )​

Answer 1

Resposta:Segue as contas abaixo na explicação

Explicação passo-a-passo:

a)a1=48,q=a2/a1--->q=12/48:12/12--->q=1/4,Sn=?

Sn=a1/1-q

Sn=48/1-1/4

Sn=48/4/4-1/4

Sn=48/3/4

Sn=48/12

Sn=4

b)a1=75,q=a2/a1--->q=15/75:15/15--->q=1/5,Sn=?

Sn=a1/1-q

Sn=75/1-1/5

Sn=75/5/5-1/5

Sn=75/4/5

Sn=75/20:5/5

Sn=15/4

c)a1=-98,q=a2/a1--->q=14/-98:14/14--->q=-1/7,Sn=?

Sn=a1/1-q

Sn=-98/1-(-1/7)

Sn=-98/1+1/7

Sn=-98/7/7+1/7

Sn=-98/8/7

Sn=-98/56:14/14

Sn=-7/4

d)a1=175,q=a2/a1--->q=-35/175:35/35--->q=-1/5,Sn=?

Sn=a1/1-q

Sn=175/1-(-1/5)

Sn=175/1+1/5

Sn=175/5/5+1/5

Sn=175/6/5

Sn=175/30:5/5

Sn=35/6

e)a1=-80,q=a2/a1--->q=-20/-80:20/20--->q=-1/4,Sn=?

Sn=a1/1-q

Sn=-80/1-(-1/4)

Sn=-80/1+1/4

Sn=-80/4/4+1/4

Sn=-80/5/4

Sn=-80/20

Sn=-4

f)a1=-648,q=a2/a1--->q=-72/-648:-72/-72--->q=1/9,Sn=?

Sn=a1/1-q

Sn=-648/1-1/9

Sn=-648/9/9-1/9

Sn=-648/8/9

Sn=-648/72

Sn=-9