Question

Determine o trigésimo primeiro termo da P.A. (15, 20, 25,...): *

d) 160
a) 165
b) 155
c) 170
​

Answer 1

$\mathrm{Progress\tilde{a}o\ aritm\acute{e}tica}\Longrightarrow\{a_1,a_2,a_3,\dots\}\Longrightarrow\{15,20,25,\dots\}$

$\boxed{a_n=a_k+(n-k)r}\Longleftarrow \text{Termo geral de uma PA.}$

$\mathrm{Primeiramente,\ \acute{e}\ preciso\ calcular\ a\ raz\tilde{a}o\ da}\ \text{PA:}$

$a_2=a_1+r\Longrightarrow r=a_2-a_1=20-15\ \therefore\ \boxed{r=5}$

$\mathrm{Agora,\ \acute{e}\ poss\acute{\i}vel\ calcular\ o\ trig\acute{e}simo\ primeiro}\ \text{termo:}$

$a_{31}=a_1+30r\Longrightarrow a_{31}=15+30(5)\ \therefore\ \boxed{a_{31}=165}$

$\text{Letra A.}$