Question

numa PA em que a6=2 e a38=10 Qual é a soma dos 20 primeiros termos dessa PA? a)120/3 b)125/4 c)150/3 d)125/2 e)100

Answer 1

$\left \{ {{a_6=a_1+5r} \atop {a_3_8=a_1+37r}} \right. \\\\\ \left \{ {{2=a_1+5r} \atop {10=a_1+37r}} \right. \\\\ -2+10 = -a_1+a_1-5r+37r\\\\\ 8=32r\\\\\ r=\frac{8}{32}\\\\ \boxed{r=\frac{1}{4}}$

$a_6=a_1+5r\\\\ 2=a_1+\frac{5}{4}\\\\ a_1=2-\frac{5}{4}\\\\ \boxed{a_1=\frac{3}{4}}$

Determinando o vigésimo termo

$a_2_0=a_1+19r\\\\ a_2_0=\frac{3}{4}+\frac{19}{4}\\\\ \boxed{a_2_0=\frac{22}{4}}$

Somatória:

$\boxed{S_n=\frac{(a_1+a_n)*n}{2}}\\\\\ S_2_0=\frac{(\frac{3}{4}+\frac{22}{4})*20}{2}\\\\ S_2_0=\frac{25}{4}*10\\\\\ \boxed{S_2_0=\frac{125}{2}}$

Alternativa D)