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?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
The differences between consecutive terms are not all equal; the last difference is -3.
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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