DIK U2=3/2 dan deret tak hingga adalah 6, tentukan rasio dan suku pertama !.... Question from @mirzanad21

October 2018 2 15 Report

DIK U2=3/2 dan deret tak hingga adalah 6, tentukan rasio dan suku pertama !

Takamori37 Mengenal deret tak hingga,
$\boxed{S_\infty=\frac{a}{1-r}}$
Maka,
$U_2=\,^3/_2 \\ ar=\,^3/_2 \\ \displaystyle a=\frac{3}{2r}$
Sehingga, didapat:
$$\begin{align} S_\infty&=6 \\ \frac{a}{1-r}&=6 \\ \frac{\frac{3}{2r}}{1-r}&=6 \\ \frac{3}{2r(1-r)}&=6 \\ \frac{1}{r(1-r)}&=6\times\frac{2}{3} \\ \frac{1}{r(1-r)}&=4 \\ 1&=4r(1-r) \\ 1&=4r-4r^2 \\ 4r^2-4r+1&=0 \\ (2r-1)^2&=0 \\ 2r-1&=0 \\ r&=\frac{1}{2} \end{align}$
Sehingga,
Dengan r = 1/2
Didapat:
$\displaystyle a=\frac{3}{2r} \\\\ a=\frac{3}{2\times\, ^1/_2} \\\\ a=\frac{3}{1} \\\\ a=3$

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Takamori37 Jawaban diedit. Silakan refresh untuk leboh lanjut

alvinteguh S∞ = a / 1 - r = 6
a.r = 3/2
a = 3/2r
substitusi
3/2r / 1 - r = 6
3/2r = 6 - 6r
3 = 12r - 12r²
12r - 12r² - 3 = 0
-12r² + 12r - 3 = 0
12r² - 12r + 3 = 0
(6r - 3) (2r - 1) = 0
r = 1/2
substitusi
a = 3/2r
a = 3/(2.1/2)
= 3/1 = 3

1 votes Thanks 1

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Berapah nilai dari r = 3/4/6-6r

Berapakah Nilai r jika : (6-6r)r =3/2

Berapakah Nilai dari : (6-6r)r =3/2

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