Which statement is correct for the three terms (a − 2b, a + b, a + 4b)?
Answer and explanation
Correct answer: They are in AP and d = 3b.
To test three symbolic terms for an arithmetic progression, calculate the two consecutive differences. The first is (a + b) − (a − 2b) = 3b. The second is (a + 4b) − (a + b) = 3b. These differences are identical for all values of a and b, so the three terms are always consecutive terms of an AP with common difference d = 3b. Therefore option A is correct. The quantity a cancels in both subtractions, so it cannot be the common difference. No extra condition such as a = b is required, and the equal differences disprove the claim that the terms are not in AP.
Frequently asked questions
What is the correct answer to this question?
They are in AP and d = 3b.
Why is this the correct answer?
To test three symbolic terms for an arithmetic progression, calculate the two consecutive differences. The first is (a + b) − (a − 2b) = 3b. The second is (a + 4b) − (a + b) = 3b. These differences are identical for all values of a and b, so the three terms are always consecutive terms of an AP with common difference d = 3b. Therefore option A is correct. The quantity a cancels in both subtractions, so it cannot be the common difference. No extra condition such as a = b is required, and the equal differences disprove the claim that the terms are not in AP.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
