Which conclusion is correct for the sequence (13, 2x+1, 4x-5)?
Answer and explanation
Correct answer: It is not an arithmetic progression for any x
For three terms to be in an arithmetic progression, twice the middle term must equal the sum of the first and third terms: 2(2x+1)=13+(4x-5). Simplifying gives 4x+2=4x+8, hence 2=8, which is impossible for every x. Therefore no value of x makes the sequence an AP, so option D is correct.
Frequently asked questions
What is the correct answer to this question?
It is not an arithmetic progression for any x
Why is this the correct answer?
For three terms to be in an arithmetic progression, twice the middle term must equal the sum of the first and third terms: 2(2x+1)=13+(4x-5). Simplifying gives 4x+2=4x+8, hence 2=8, which is impossible for every x. Therefore no value of x makes the sequence an AP, so option D is correct.
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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