For which (y) are (5y+2, 3y+10, y+18) in an arithmetic progression?

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.