The sequence (m+1, 3m−2, 6m−8) is stated not to be an arithmetic progression. For which value of m will this statement become false?
Answer and explanation
Correct answer: 6
The statement becomes false when the three displayed terms do form an arithmetic progression. Apply the middle-term condition: 2(3m−2)=(m+1)+(6m−8). This gives 6m−4=7m−7, and therefore m=3. Substituting m=3 produces the terms 4, 7, and 10, with differences 3 and 3. Hence the corrected answer is 3. None of the original options contained 3, so the options have been repaired by replacing the distractor 6 with 3. The other listed values do not make the two consecutive differences equal.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The statement becomes false when the three displayed terms do form an arithmetic progression. Apply the middle-term condition: 2(3m−2)=(m+1)+(6m−8). This gives 6m−4=7m−7, and therefore m=3. Substituting m=3 produces the terms 4, 7, and 10, with differences 3 and 3. Hence the corrected answer is 3. None of the original options contained 3, so the options have been repaired by replacing the distractor 6 with 3. The other listed values do not make the two consecutive differences equal.
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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