Seutas tali dipotong-potong menjadi 8 bagian dengan panjang potongan-potongan tersebut membentuk barisan geometri. Jika panjang potongan terpendek 3 cm dan terpanjang 384 cm, panjang tali sebelum dipotong adalah ..

The rope is cut into $n=8$ pieces. The lengths form a geometric sequence.
The shortest piece is the first term, $a_1 = 3$ cm.
The longest piece is the eighth term, $a_8 = 384$ cm.

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$.
Substitute the values for $a_8$, $a_1$, and $n$:

Divide both sides by 3:

To find $r$, we take the 7th root of 128:

Since $2^7 = 128$, the common ratio is:

The total length of the rope before it was cut is the sum of all 8 pieces. The formula for the sum of the first $n$ terms of a geometric sequence is $S_n = \frac{a_1(r^n - 1)}{r - 1}$.
Substitute the values $a_1 = 3$, $r = 2$, and $n = 8$:

The total length of the rope before it was cut is 765 cm.

The calculated sum is 765 cm, which corresponds to option E.

The final answer is $\text{E. } 765$.