Question

32. Determine a P.A. em que se verificam as relações a12 + a21 = 302 e a23 + a46 = 446.? me ajudeeem por favor!

Answer 1

$\mathrm{a_{12}+a_{21}=302}\\ \mathrm{a_1+11r+a_1+20r=302\ \to\ \boxed{\mathrm{2a_1+31r=302}}\ \mathbf{(I)}}\\\\ \mathrm{a_{23}+a_{46}=446}\\ \mathrm{a_1+22r+a_1+45r=446\ \to\ \boxed{\mathrm{2a_1+67r=446}}\ \mathbf{(II)}}\\\\ \mathbf{Somando\ II\ com\ (-1).I:}\\\\ \mathrm{2a_1+67r-2a_1-31r=446-302}\\ \mathrm{36r=144\ \to\ r=144/36\ \to\ \boxed{\mathrm{r=4}}}\\\\ \mathbf{Substituindo\ o\ valor\ de\ r\ em\ I:}\\\\ \mathrm{2a_1+31.4=302\ \to\ 2a_1=302-124}\\ \mathrm{2a_1=178\ \to\ a_1=178/2\ \to\ \boxed{\mathrm{a_1=89}}}$

$\boxed{\boxed{\mathbf{PA=\{89,93,97,101,105,109,113,\dots\}}}}}$