Question

Determine a soma dos termos de cada PA:

a) (3,11,19...,115)

b)(86,83,80...,35)

c)(-8,-5,-2,...22)

Answer 1

a
a1 = 3
a2 = 11
r = 11 - 3 = 8 ***
an = 115
115 = 3 + ( n-1)8
115 - 3 = 8n - 8
112 + 8 = 8n
8n = 120
n = 15 ***
S15 = ( 3 + 115) * 7,5
S15 = 118 * 7,5 = 885 ****

b
a1 = 86
a2 =83
r = 83 - 86 = -3 ****
an = 35
35 = 86 + ( n-1)(-3)
35 - 86 = -3n + 3
-51 - 3 = -3n
-54 = -3n
3n = 54
n = 54/3  = 18 ****
S18  = ( 86 + 35)* 9 =
S18 =121 * 9 = 1089 ****
c
a1 = -8
a2 -5
r = -5 - ( -8 ) = -5 + 8 = 3 ****
an = 22

22 = -8 + ( n - 1) 3
22 +8 = 3n - 3
30 + 3 = 3n
3n = 33
n = 11 *****
S11 = ( -8 + 22)5,5
S11 = 14 * 5.5 =77******