A student says that the sequence 25, 21, 17, 14 is an arithmetic progression because its terms are decreasing. What is the error in the student's statement?

Correct answer: The differences between consecutive terms are not all equal; the last difference is -3.

In an AP, every consecutive difference must be equal. Here, 21-25=-4 and 17-21=-4, but 14-17=-3. Hence it is not an AP. Exam tip: check at least all adjacent differences, not merely whether terms increase or decrease.