jika a+2 , a-1 , a-7 membentuk barisan geometri , maka rasio nya adalah ... ini gmna yah cara nya .. tolong bantuan nya yah teman

Deret Geometri

Un =
[tex]ar {}^{n - 1} [/tex]
U1 = a = a + 2
U2 = ar = a - 1
U3 = ar² = a - 7

[tex] \frac{u1}{u2} = \frac{a}{ar} = \frac{a + 2}{a - 1} \\ \\ \frac{1}{r} = \frac{a + 2}{a - 1} \\ \\ a - 1 = r(a + 2)[/tex]

[tex] \frac{u2}{u3} = \frac{ar}{a {r}^{2} } = \frac{a - 1}{a - 7} \\ \\ \frac{1}{r} = \frac{a - 1}{a - 7} \\ \\ a - 7 = r(a - 1)[/tex]

[tex]a - 1 = r(a + 2) \\ a - 7 = r(a - 1) \\ - - - - - - - -( \div ) \\ \\ \frac{a - 1}{a - 7} = \frac{a + 2}{a - 1} \\ \\ (a - 1)(a - 1) = (a + 2)(a - 7) \\ {a}^{2} - a - a + 1 = {a}^{2} - 7a + 2a - 14 \\ {a}^{2} - 2a + 1 = {a}^{2} - 5a - 14 \\ {a}^{2} - 2a - {a}^{2} + 5a = - 14 - 1 \\ 3a = - 15 \\ a = - 5[/tex]

U1 = a + 2 = -5 + 2 = -3
U2 = a - 1 = -5 - 1 = -6
U3 = a - 7 = -5 - 7 = -12

r = U2/U1= -6/(-3( = 2

Jadi, rasio = 2.

[Barisan Geometri]

Perbandingan Rasio
U2/U1 = U3/U2
(a - 1)/(a + 2) = (a - 7)/(a - 1)
(a - 1)² = (a + 2)(a - 7)
a² - 2a + 1 = a² - 5a - 14
3a = -15
a = -5

Substitusi..
Rasio = U2/U1
Rasio = (a - 1)/(a + 2)
Rasio = (-5 - 1)/(-5 + 2)
Rasio = 2