Question

Determine cada termo da PG (a+3, 5a-3, 8a).

Answer 1

q = a 2 / a1
q = a 3 / a 2
5 a - 3  / a + 3 = 8 a / 5 a - 3
8 a (a + 3) = (5 a - 3 ) (5 a - 3)
8 a² + 24 a = 25 a² - 15 a - 15 a + 9
8 a² - 25 a² + 24 a = - 30 a + 9
-17 a² + 24 a + 30 a - 9 = 0
-17 a² + 54 a - 9 = 0
Δ = b² - 4.a.c
Δ = 54² - 4 . -17 . - 9
Δ = 2916 - 612
Δ  = 2304 ⇒ √ 2304 = 48
x´= - b + ou - 48/2. -17
x´= -54 + 48/-34
x´= -6/ - 34
x´= 3/17
x´´ = -54 - 48 / - 17 . 2
x´´ = -102/- 34
x´´ = 3

a 1 = a + 3
a 1 = 3 + 3 = 6

a 2 = 5 a - 3
a 2 = 5 . 3 - 3
a 2 = 15 - 3
a 2 = 12

a 3 = 8 a
a 3 = 8.3
a 3 = 24
P.G(6,12,24)