Resolução dos exercícios de Haamon e Millene

1-Determine o número de termos da P.A (-3,2,6,...,114).


N=?                                                    An=a1 + (n- 1).r
An=114                                              114=-3 + (n-1).5
A1=-3                                                114=-3 + 5n - 5
R=6-1=5                                            114=5n - 8
                                                          114-8 = 5n
                                                           106=5n
                                                           106 =  21= n
                                                            5




2-numa estrada existe três telefones instalados no acostamento,um no km 3 e o outro no km 88 .entre eles
serão colocados mais 15 telefones,mantendo-se entre dois telefones consecutivos sempre a mesma distância.Determine em quais marcos quilométricos deverão ficar esses telefones.


N=17                                                An=a1+(n-1).r
An=88                                              88=3+(17-1).r
A1=3                                                88=3+16r
R= ?                                                  88-3=16r
                                                          85 = 5 = R
                                                          16


3-Quantos múltiplos de 5 podemos achar com 3 algarismos?


N= ?                                                  An=a1+ (n-1).r
An=995                                             995=100+(n - 1).5
A1=100                                             995=100+5n-1
R=6-1=5                                            995=5n-99
                                                          995+99=5n
                                                          1094=5n
                                                          1094 = 219=n
                                                            5


4-Determine o 5º termo da P.A(8,20, ...).


8,20,32,44,56


5-Achar o número de múltiplos de 6 compreendidos entre 25 e 250 .


A1=30                                               An=a1+(n-1).r
An=240                                             240=30(n-1).6
N=?                                                   240=30+6n - 6
R=6                                                   240=24+6n
                                                          240-24=6n
                                                          216=6n
                                                          216  = n = 36
                                                           6