Question

Determine a soma dos termos de cada PA (86,83,80,...,35)

Answer 1

35= 86 +(n-1) .-3
35 = 86 -3n +3
3n = 86 +3 - 35
3n = 54 
n = 54/3
n = 18
sn = (86 +35) .18/2
sn = 121 .18/2
sn =  2178/2
sn =1089 

Answer 2

Número de termos:

$a_1 = 86 \\ r = -3 \\ a_n = 35 \\ n = \,? \\ \\ a_n = a_1+(n-1)r \\ \\ 35 = 86 + (n-1)(-3) \\ \\ 35 = 86 -3n + 3 \\ \\ 3n = 86 - 35 + 3 \\ \\ 3n = 54 \\ \\ n = \frac{54}{3} \\ \\ n = 18$

Soma dos termos:

$a_1= 86 \\ a_{18} = 35 \\ n = 18 \\ \\ S_{n} = \frac{(a_1+a_n)n}{2} \\ \\ S_{18} = \frac{(86+35).18}{2} \\ \\ S_{18} = 121.9 \\ \\ S_{18} = 1089$