1- Calcule a soma dos termos das PAs abaixo:
a-Dos 20 primeiros termos ( 5,8,11,...,62)
b -Dos 15 primeiros termos ( -4,-2,0,...24)
c - Dos 100 primeiros termos ( 3,6,...,300)
d - Dos 25 primeiros termos ( 250,244,...,106)
e - Dos 17 primeiros termos ( 5,8,11,...,6)
f - Dos 20 primeiros termos ( -5,-10,...)
g - Dos 44 primeiros termos ( 8,5,2,...)
h - Dos 120 primeiros termos (0,8; 0,11 ; 0,14;...)
i - Dos 16 primeiros termos (-30, -24,...).........
Soluções para a tarefa
Resposta:Segue as contas abaixo na explicação
Explicação passo-a-passo:
Questão 1
a)a1=5,r=a2-a1--->r=8-5--->r=3,n=20,a20=?,S20=?
an=a1+(n-1).r Sn=(a1+an).n/2
a20=5+(20-1).3 S20=(5+62).20/2
a20=5+19.3 S20=67.20/2
a20=5+57 S20=67.10
a20=62 S20=670
b)a1=-4,r=a2-a1--->r=-2-(-4)--->r=-2+4---->r=2,n=15,a15=?,S15=?
an=a1+(n-1).r Sn=(a1+an).n/2
a15=-4+(15-1).2 S15=(-4+24).15/2
a15=-4+14.2 S15=20.15/2
a15=-4+28 S15=10.15
a15=24 S15=150
c)a1=3,r=a2-a1--->r=6-3--->r=3,n=100,a100=?,S100=?
an=a1+(n-1).r Sn=(a1+an).n/2
a100=3+(100-1).3 S100=(3+300).100/2
a100=3+99.3 S100=303.100/2
a100=3+297 S100=303.50
a100=300 S100=15150
d)a1=250,r=a2-a1--->r=244-250--->r=-6,n=25,a25=?,S25=?
an=a1+(n-1).r Sn=(a1+an).n/2
a25=250+(25-1).(-6) S25=(250+106).25/2
a25=250+24.(-6) S25=356.25/2
a25=250-144 S25=178.25
a25=106 S25=4450
e)a1=5,r=a2-a1--->r=8-5--->r=3,n=17,a17=?,S17=?
an=a1+(n-1).r Sn=(a1+an).n/2
a17=5+(17-1).3 S17=(5+53).17/2
a17=5+16.3 S17=58.17/2
a17=5+48 S17=29.17
a17=53 S17=493
f)a1=-5,r=a2-a1--->r=-10-(-5)--->r=-10+5---->r=-5,n=20,a20=?,S20=?
an=a1+(n-1).r Sn=(a1+an).n/2
a20=-5+(20-1).(-5) S20=[-5+(-95)].20/2
a20=-5+19.(-5) S20=[-5-95].20/2
a20=-5-95 S20=[-100].20/2
a20=-100 S20=[-100].10
S20=-1000
g)a1=8,r=a2-a1--->r=5-8--->r=-3,n=44,a44=?,S44=?
an=a1+(n-1).r Sn=(a1+an).n/2
a44=5+(44-1).(-3) S44=[5+(-127)].44/2
a44=5+43.(-3) S44=[5-127].44/2
a44=5-132 S44=[-122].44/2
a44=-127 S44=[-122].22
S44=-2684
h)a1=0,08;r=a2-a1--->r=0,11-0,08--->r=0,03;n=120,a120=?,S120=?
an=a1+(n-1).r Sn=(a1+an).n/2
a120=0,08+(120-1).0,03 S120=(0,08+3,65).120/2
a120=0,08+119.0,03 S120=3,73.120/2
a120=0,08+3,57 S120=3,73.60
a120=3,65 S120=223,80
i)a1=-30,r=a2-a1--->r=-24-(-30)--->r=-24+30--->r=6,n=16,a16=?,S16=?
an=a1+(n-1).r Sn=(a1+an).n/2
a16=-30+(16-1).6 S16=(-30+45).16/2
a16=-30+15.5 S16=15.16/2
a16=-30+75 S16=15.8
a16=45 S16=120