[tex]\large\text{$ A ~soma ~do ~terceiro~ termo ~com ~o~ quarto~termo ~ \Rightarrow ~ S = \dfrac{1}{2} $}[/tex]
[tex]\Large\text{$ Progress\tilde{a}o ~Aritm\acute{e}tica $}[/tex]
Valores dados no problema:
[tex]a2 = -2\\\\r = \dfrac{3}{2}[/tex]
Encontrar o valor do termo a3 ( terceiro termo ).
[tex]an = ak + ( n - k ).r \\\\\\ -2 = a3 + ( 2 - 3 ) . \dfrac{3}{2}\\\\\\ -2 = a3 + (-1 ) . \dfrac{3}{2}\\\\\\-2 = a3 - \dfrac{3}{2}\\\\\\-2 + \dfrac{3}{2} = a3\\\\\\a3 = -\dfrac{1}{2}[/tex]
Encontrar o valor do termo a4 ( terceiro termo ).
[tex]an = ak + ( n - k ).r\\\\\\-2 = a4 + ( 2 - 4 ) . \dfrac{3}{2}\\\\\\-2 = a4 + (-2 ) . \dfrac{3}{2}\\\\\\-2 = a4 - 3\\\\-2 + 3 = a4\\\\a4 = 1[/tex]
Soma dos termos a3 + a4:
[tex]S = -\dfrac{1}{2} + 1\\\\\\S = \dfrac{1}{2}[/tex]
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