Step 1 :The plant's growth follows an arithmetic sequence. This means that the difference between the heights of the plant in consecutive weeks is constant.
Step 2 :We can find this difference by subtracting the height of the plant in the third week from the height in the fourth week. \(10 - 8 = 2\)
Step 3 :Once we have this difference, we can multiply it by the number of weeks minus 3 (since we already know the height at week 3) and add the result to the height at week 3 to find the height at week 25. \((25 - 3) * 2 + 8 = 52\)
Step 4 :Final Answer: The plant will be \(\boxed{52}\) centimeters tall after 25 weeks.