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Class 10MathematicsArithmetic Progressions (AP)Introduction to APs and common difference.Medium
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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.

Related tags

Arithmetic ProgressionAlgebraic ConditionCommon DifferenceIntroduction To Aps And Common Difference.Introduction To Aps And Common DifferenceArithmetic Progressions (Ap)Arithmetic Progressions ApMathematics
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10 more MCQs
  1. 1What is the common difference in the sequence 3, 7, 11, 15, …?
  2. 2In an arithmetic progression, how is the common difference (d) found?
  3. 3What is the common difference in (10,8,6,4,\ldots)?
  4. 4Which sequence is an arithmetic progression?
  5. 5What is the common difference of (6,6,6,6,\ldots)?
  6. 6What is the first term of the arithmetic progression (12,17,22,27,\ldots)?
  7. 7In the sequence (4,9,14,\Box,24,\ldots), what is the value of (\Box)?
  8. 8Which sequence is not an arithmetic progression?
  9. 9If the first term of an arithmetic progression is (a=5) and the common difference is (d=3), what is the second term?
  10. 10What is the common difference in (-3,1,5,9,\ldots)?
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