The first term in a geometric sequence is 512 the fourth term is 1 find the first 4term

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$.
Given $a_1 = 512$ and $a_4 = 1$.

$$a_4 = a_1 \cdot r^{4-1}$$ $$1 = 512 \cdot r^3$$

Divide both sides by 512:

$$r^3 = \frac{1}{512}$$

Take the cube root of both sides:

$$r = \sqrt[3]{\frac{1}{512}}$$ $$r = \frac{1}{8}$$

Using the common ratio $r = \frac{1}{8}$ and the first term $a_1 = 512$:

$$a_1 = 512$$ $$a_2 = a_1 \cdot r = 512 \cdot \frac{1}{8} = 64$$ $$a_3 = a_2 \cdot r = 64 \cdot \frac{1}{8} = 8$$ $$a_4 = a_3 \cdot r = 8 \cdot \frac{1}{8} = 1$$

The first 4 terms of the geometric sequence are:

$$512, 64, 8, 1$$