Jika tiga bilangan \( q, s, \) dan \(t\) membentuk barisan geometri, maka \( \frac{q+s}{q+2s+t} = \cdots \)
- \( \frac{q}{q+t} \)
- \( \frac{s}{s+t} \)
- \( \frac{s}{q+s} \)
- \( \frac{q}{s+t} \)
- \( \frac{t}{q+t} \)
Pembahasan:
Diketahui bilangan \( q, s, \) dan \(t\) membentuk barisan geometri, sehingga berlaku:
\begin{aligned} U_n &= ar^{n-1} \\[8pt] U_2 &= ar^{2-1} = ar \\[8pt] s &= qr \\[8pt] U_3 &= ar^{3-1} = ar^2 \\[8pt] t &= qr^2 = sr \Leftrightarrow r = \frac{t}{s} \\[8pt] \frac{q+s}{q+2s+t} &= \frac{q+qr}{q+2qr+qr^2} = \frac{1+s}{1+2r+r^2} \\[8pt] &= \frac{1+r}{(1+r)^2} = \frac{1}{1+r} = \frac{1}{1+\frac{t}{s}} \\[8pt] &= \frac{1}{\frac{s+t}{s}} = \frac{s}{s+t} \end{aligned}
Jawaban B.