Which sequence is not an arithmetic progression even though the first two differences look equal?
Answer and explanation
Correct answer: (2, 6, 10, 15, …)
The defining condition for an arithmetic progression is that every consecutive difference must be the same, not merely the first one or two. In option A, the first differences are 6 − 2 = 4 and 10 − 6 = 4, but the next difference is 15 − 10 = 5. Because the difference changes from 4 to 5, this sequence is not an AP. In option B, all displayed differences are 5; in option C, they are −4; and in option D, they are 0. Therefore option A is the only sequence that fails the definition. This question emphasizes why all available consecutive differences should be checked before classifying a sequence.
Frequently asked questions
What is the correct answer to this question?
(2, 6, 10, 15, …)
Why is this the correct answer?
The defining condition for an arithmetic progression is that every consecutive difference must be the same, not merely the first one or two. In option A, the first differences are 6 − 2 = 4 and 10 − 6 = 4, but the next difference is 15 − 10 = 5. Because the difference changes from 4 to 5, this sequence is not an AP. In option B, all displayed differences are 5; in option C, they are −4; and in option D, they are 0. Therefore option A is the only sequence that fails the definition. This question emphasizes why all available consecutive differences should be checked before classifying a sequence.
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.
