To find the sum of the first 10 terms of a geometric sequence, we can use the formula for the sum of the first $n$ terms:

$S_n = a \frac{1 - r^n}{1 - r}$

Where:

• $S_n$ is the sum of the first $n$ terms.
• $a$ is the first term of the sequence.
• $r$ is the common ratio.
• $n$ is the number of terms.

For the given sequence 4, 2, 1,...:

• $a = 4$
• $r = \frac{2}{4} = \frac{1}{2}$
• $n = 10$

Now, substitute the values into the formula:

$S_{10} = 4 \frac{1 - \left(\frac{1}{2}\right)^{10}}{1 - \frac{1}{2}}$

Simplify the expression:

[ S_{10} = 4