Question

determine a soma dos termos de cada PA
a) ( -8,-5,-2,...22)

Answer 1

an= a1 +(n-1).r
22= -8+(n-1). 3
22= -8 + 3n -3
22+8+3= 3n
33=3n
n= 11

$Sn= \frac{(an+a1).n}{2}$

$Sn= \frac{(22-8).11}{2} \\ \\ Sn= \frac{14*11}{2} \\ \\ Sn= \frac{154}{2} \\ \\ Sn= 77$

Answer 2

a1 = - 8
a2 = - 5

r = a2 - a1 
r = - 5 - ( - 8)
r = - 5 + 8
r = 3

an = 22

an = a1 + (n - 1).r
22 = - 8 + (n - 1).3
22 + 8 = 3n - 3
30 = 3n - 3
30 + 3 = 3n
33 = 3n
3n = 33
n = 33/3
n = 11

Sn = (a1 + an).n
             2

Sn = (- 8 + 22).11
                 2
Sn = 14. 11
            2
Sn = 7.11
Sn = 77

Resp.: S11 = 77