For which (y) are (5y+2, 3y+10, y+18) in an arithmetic progression?
Answer and explanation
Correct answer: For every (y)
In an arithmetic progression, the differences between consecutive terms must be equal. Here, second term − first term = (3y+10)−(5y+2)=−2y+8. Also, third term − second term = (y+18)−(3y+10)=−2y+8. Since the two differences are equal for every (y), the correct answer is every (y). Although (y=0) and (y=4) also work, the AP is not restricted to those values. Exam tip: For three terms in AP, twice the middle term equals the sum of the first and third terms.
Frequently asked questions
What is the correct answer to this question?
For every (y)
Why is this the correct answer?
In an arithmetic progression, the differences between consecutive terms must be equal. Here, second term − first term = (3y+10)−(5y+2)=−2y+8. Also, third term − second term = (y+18)−(3y+10)=−2y+8. Since the two differences are equal for every (y), the correct answer is every (y). Although (y=0) and (y=4) also work, the AP is not restricted to those values. Exam tip: For three terms in AP, twice the middle term equals the sum of the first and third terms.
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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