São dados os elementos a20 = 17 e a23 = 19 de uma P A qual é a razão desta progressão

São dados os elementos a20 = 17 e a23 = 19 de uma P A qual é a razão desta progressão



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    Vamos montar um sistema

    a_2_0=a_1+19r a_2_3=a_1+22r

    Multiplicando a primeira coluna por -1 e somando com a debaixo:

    17=a_1+19r 19=a_1+22r -17+19=-a_1+a_1-19r+22r 2=3r boxed{r=frac{2}{3}}

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    Utilize a Frmula do Termo Geral das PA s:

    boxed{a_n=a_1+(n-1).r}#10;#10;a_{23}=a_1+22r#10;a_{20}=a_1+19r#10;#10;a_{23}-a_{20}=a_1+22r-(a_1+19r)=19-17#10;#10;a_1+22r-a_1-19r=2#10;#10;3r=2#10;#10;boxed{r=frac{2}{3}}


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+ 22 = 25