Question

02) Dtermine:

A) o 6º termo da P.A.(-4, 1, ...)

B) o 5º termo da P.A.(5, 2, ...)

C) o 4º termo da P.A.(a+4b, a+2b, ...)​

Answer 1

$\large\boxed{\begin{array}{l}\sf Chama-se\,Progress\tilde ao\,aritm\acute etica\,a\,toda\,sequ\hat encia\\\sf onde~cada~termo,a\,partir\,do\,segundo,\\\sf \acute e\,igual\,ao\,termo\,anterior\,somado\,com\,uma\,constante\\\sf chamada\,raz\tilde ao\,da\,progress\tilde ao\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\sf Classificac_{\!\!,}\tilde ao\,de\,uma\,PA}\\\sf \boldsymbol{crescente:}~\sf quando\,r>0.\\\sf exemplo:(1,3,5,7)\\\sf r=a_2-a_1=a_3-a_2=a_4-a_3=2\\\boldsymbol{decrescente:}~\sf quando\,r<0.\\\sf exemplo:(9,7,5,3,1)\\\sf r=a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=-2\\\boldsymbol{constante:}~\sf quando\,r=0.\\\sf exemplo:(5,5,5,5)\\\sf r=a_2-a_1=a_3-a_2=a_4-a_3=0\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\sf Termo\,geral\,da\,PA}\\\underline{\sf Em\,func_{\!\!,}\tilde ao\,de\,um\,termo\,p\,qualquer}\\\huge\boxed{\boxed{\boxed{\boxed{\sf a_n=a_p\!+\!(n-p)\!\cdot\! r}}}}\\\sf a_n\longrightarrow termo\,geral\\\sf a_p\longrightarrow termo\,qualquer\\\sf n\longrightarrow n\acute umero\,de\,termos\\\sf r\longrightarrow raz\tilde ao\,da\,progress\tilde ao\end{array}}$

$\Large\boxed{\begin{array}{l}\rm A)~\sf (-4,1,\dotsc)\\\sf r=1-[-4]=1+4=5\\\sf a_6=a_2+4r\\\sf a_6=1+4\cdot5\\\sf a_6=1+20\\\sf a_6=21\\\rm B)~\sf(5,2,\dotsc)\\\sf r=2-5=-3\\\sf a_5=a_2+3r\\\sf a_5=2+3\cdot(-3)\\\sf a_5=2-9\\\sf a_5=-7\\\rm C)~\sf (a+4b,a+2b,\dotsc)\\\sf r=a+2b-(a+4b)\\\sf r=\backslash\!\!\!a+2b-\backslash\!\!\!a-4b\\\sf r=-2b\\\sf a_4=a_2+2r\\\sf a_4=a+2b+2\cdot(-2b)\\\sf a_4=a+2b-4b\\\sf a_4=a-2b\end{array}}$