If (x, x+6, 3x−2) are in an arithmetic progression, what is the third term?
Answer and explanation
Correct answer: 19
Use the condition for three consecutive arithmetic-progression terms: twice the middle term equals the sum of the first and third terms. Thus 2(x+6)=x+(3x−2). Expanding gives 2x+12=4x−2, so 14=2x and x=7. The third term is therefore 3x−2=3(7)−2=21−2=19. Hence option A is correct. The original options and explanation were inconsistent: the calculation actually gives x=7 and third term 19, not x=9 or 25. The corrected options now include 19 and retain distinct distractors.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
Use the condition for three consecutive arithmetic-progression terms: twice the middle term equals the sum of the first and third terms. Thus 2(x+6)=x+(3x−2). Expanding gives 2x+12=4x−2, so 14=2x and x=7. The third term is therefore 3x−2=3(7)−2=21−2=19. Hence option A is correct. The original options and explanation were inconsistent: the calculation actually gives x=7 and third term 19, not x=9 or 25. The corrected options now include 19 and retain distinct distractors.
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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