O problema nos diz que:
[tex]a_1=-2\hspace{2.0cm}a_n=43\hspace{2.0cm}n=2+8=10[/tex]
Utilizando a fórmula do termo geral, temos:
[tex]a_n=a_1+(n-1)r\\\\
43=-2+(10-1)r\\\\
45=9r\\\\
r=5[/tex]
Agora podemos calcular os 8 números:
[tex]a_2=a_1+r\Longrightarrow a_2=-2+5=3\\\\
a_3=a_2+r\Longrightarrow a_3=3+5=8\\\\
a_4=a_3+r\Longrightarrow a_4=8+5=13\\\\
a_5=a_4+r\Longrightarrow a_5=13+5=18\\\\
a_6=a_5+r\Longrightarrow a_6=18+5=23\\\\
a_7=a_6+r\Longrightarrow a_7=23+5=28\\\\
a_8=a_7+r\Longrightarrow a_8=28+5=33\\\\
a_9=a_8+r\Longrightarrow a_9=33+5=38[/tex]
Então podemos escrever a PA:
[tex](-2,5,8,13,18,23,28,33,38,43)[/tex]
