Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct?

1. ka, kb, kc are in AP

2. k - a, k - b, k - c are in AP

3.  are in AP

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This question was previously asked in
NDA (Held On: 17 Nov 2019) Maths Previous Year paper
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  1. 1 and 2 only
  2. 2 and 3 only
  3. 1 and 3 only
  4. 1, 2, and 3

Answer (Detailed Solution Below)

Option 4 : 1, 2, and 3
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Detailed Solution

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Concept:

1. If a, b and c are in A.P 

  • Then ka, kb, kc are in AP
  • eg. 2, 4, 6 are in A.P then (2 × 2, 4 × 2, 6 × 2) = (4, 8, 12) are also in A.P

2. If a, b and c are in A.P 

  • Then k - a, k - b, k - c are in AP
  • eg. 2, 4, 6 are in A.P then (8 - 2, 8 - 4, 8 - 6) = (6, 4, 2) are also in A.P

3. If a, b and c are in A.P 

  • Then  are in AP
  • eg. 2, 4, 6 are in A.P then (2/2, 4/2, 6/2) = (1, 2, 3) are also in A.P
  • Hence, All the options are correct.

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