Question

6.Calcule a soma dos 25 termos iniciais da P. A (1, 7, 13,... )

Answer 1

a1 = 1
razão r = 7 - 1 = 6

Termo geral: an = a1 + (n-1).r
a25 = 1 + (25-1).r
a25 = 1 + 24.6
a25 = 1 + 144
a25 = 145

S25 = (a1 + an).n/2
S25 = (1 + 145).25/2
 S25 = (146).25/2
S25 = 73.25
 S25 = 1825

Resposta: a soma de 25 termos da PA é 1825

Espero ter ajudado.

Answer 2

$r=a_2-a_1\longrightarrow{r}=7-1\longrightarrow{r}=6\\\\\\a_{25}=a_1+24r\longrightarrow{a}_{25}=1+24(6)\longrightarrow{a}_{25}=145\\\\\\S_{25}=\dfrac{25(a_1+{a_{25}})}{2}\longrightarrow{S}_{25}=\dfrac{25(1+145)}{2}\longrightarrow{S}_{25}=\dfrac{25(146)}{2}\longrightarrow\\\\{S_{25}}=25(73)\longrightarrow\boxed{{S}_{25}=1825}$