Question

1°) sabendo q a sequência ( x, 3x+1, 2x+11) é uma PA, calcule a razão dessa PA.​

Answer 1

$\displaystyle r=a_n-a_{n-1}\\\\r=a_3-a_2\\r=(2x+11)-(3x+1)\\r=2x-3x+11-1\\r=-x+10\\\\r=a_2-a_1\\r=(3x+1)-x\\r=3x-x+1\\r=2x+1\\\\r=r\\-x+10=2x+1\\-x-2x=1-10\\-3x=-9\\\\x=\frac{-9}{-3}\\\\x=3\\\\\\r = -x+10\\r=-3+10\\r=7$

Com isso, a razão essa PA é 7 (r = 7).

Prova Real:

$(x, 3x+1, 2x+11) = (3, 3.3+1, 2.3+11) = (3, 10, 17)\\razao = 7$