Question

determine a razão da PG (x, x+2, x+16)

Answer 1

a1 = x
a2 = x + 2
a3 = x + 16

( x + 16)x = ( x + 2)²
x² + 16x = x² + 4x + 4
x² + 16x - x² - 4x - 4 = 0
12x - 4 = 0
12x = 4
x = 4/12  = 1/3
a1 = x =1/ 3
a2 = x + 2 =1/3  + 2/1 =  ( 1 + 6)/3 = 7/3 ***
a3 = x  + 16 =1/3 + 16/1 = ( 1 + 48)/3 = 49/3
7/3 - 1/3 = 6/3 = 2 ***
49/3 - 7/3 = 42/3 = 14 ***
q  = 7/3 : 1/3 = 7/3 * 3/1 = 21/3 = 7 ****