Task B-4.4. The first three of five numbers form an arithmetic sequence with a difference of 8, and the last four form a geometric sequence with a quotient of 2. What are the numbers?
## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_0148fcdd1c92efebb536g-22.jpg?height=176&width=526&top_left_y=1560&top_left_x=772)

The arithmetic part of the sequence can be denoted as $x-16, x-8, x$. The geometric part of the sequence can be denoted as $x-8, 2(x-8), 4(x-8), 8(x-8)$.

(2 points)

It follows that $x = 2(x-8)$, so $x = 16$.

(1 point)

The desired numbers are $0, 8, 16, 32, 64$.

(1 point)