What is the common difference of the AP 81, 72, 63, 54, ...?
Answer and explanation
Correct answer: −9
The governing concept is the common difference of an arithmetic progression, defined as the difference between any term and the immediately preceding term. Subtract the first term from the second: d = 72 − 81 = −9. Checking the next pairs gives 63 − 72 = −9 and 54 − 63 = −9, confirming that the sequence is an AP with d = −9. Therefore option B is correct. The negative sign is essential because the terms decrease as the sequence advances. Option A gives the magnitude but loses the direction, option C doubles the actual change, and option D is merely a term of the sequence rather than a difference. Thus the constant signed difference is −9.
Frequently asked questions
What is the correct answer to this question?
−9
Why is this the correct answer?
The governing concept is the common difference of an arithmetic progression, defined as the difference between any term and the immediately preceding term. Subtract the first term from the second: d = 72 − 81 = −9. Checking the next pairs gives 63 − 72 = −9 and 54 − 63 = −9, confirming that the sequence is an AP with d = −9. Therefore option B is correct. The negative sign is essential because the terms decrease as the sequence advances. Option A gives the magnitude but loses the direction, option C doubles the actual change, and option D is merely a term of the sequence rather than a difference. Thus the constant signed difference is −9.
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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