The uploaded image describes a sequence problem involving the price of a stock that decreases hourly, forming a geometric sequence. Let's break down and solve the problem.

Recognize and Describe:

• The sequence starts at 18,900 dollars.
• Each term is divided by 10, meaning the common ratio (r) is $\frac{1}{10} = 0.1$.

Classify:

• Since each term is obtained by multiplying the previous term by a constant ratio (0.1), the sequence is geometric.

Recursive Formula:

• The first term is $g_1 = 18,900$.
• The recursive formula is: $g_n = g_{n-1} \cdot r$ where $r = 0.1$.

Predict the Next Term:

The fourth term is $18.9$. To find the fifth term: $g_5 = g_4 \cdot 0.1 = 18.9 \cdot 0.1 = 1.89$

Answer:

After another hour, the stock price would be $1.89 per share.

Would you like a detailed breakdown or have questions? Here are some related questions for practice:

1. How would the formula change if the common ratio was $0.5$ instead of $0.1$?
2. Write the explicit formula for the $n$-th term of this sequence.
3. How many hours would it take for the price to drop below $\$0.01$?
4. What is the sum of the first five terms of this sequence?
5. If the initial stock price was $10,000 and the common ratio remained the same, what would be the price after 5 hours?

Tip: Always verify the common ratio in geometric sequences by dividing any term by its preceding term.