Question

Ola gente ajudem a resolver esta questao
Qual é o termo geral da sucessao 18; 15; 12; 9; 6; ...
Para facilitar a resposta correcta é: 21 - 3n. Preciso a resolução

Answer 1

$\text{Progress\~ao:}~~21;18;15;12;9;6~...\\\\\\\text{\'E uma progress\~ao aritm\'etica.}\\\\\\a_1=~\text{primeiro termo}\\\\a_2=~\text{segundo termo}\\\\a_3=~\text{terceiro termo}\\\\~~~~~~~~~~~~~~.\\~~~~~~~~~~~~~~.\\~~~~~~~~~~~~~~.\\\\a_n=~\text{n-\'esimo termo}\\\\\\q=\text{raz\~ao}$


$a_1+q=a_2\\\\a_1+2q=a_3\\\\a_1+3q=a_4\\\\~~~~~~~~.\\~~~~~~~~.\\~~~~~~~~.\\\\a_1+n\cdot q=a_n$

$\text{Logo:}\\\\\\21+n(-3)=a_n\\\\\\a_n=21+(-3n)\\\\\\\fbox{a_n=21-3n }~~\text{(termo geral)}$