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The numbers 1,5 and 25 can be three terms (not necessarily consecutive) of

Options

  1. Aonly one AP
  2. Bmore than one but finite numbers of APs
  3. Cinfinite number of APs
  4. Dfinite number of GPs

Correct answer

C. infinite number of APs

Step-by-step solution

Given, numbers 1,5,25 Let p ^ th term =1 a +( p -1) d =1 ...(1) Let q ^ th term =5 a +( q -1) d =5 ...(2) Let r^ th term =25 a+(r-1) d=25 ...(3) Applying (3) - (2) r - q =25-5=20 Applying (2) -(1) q - p =5-1=4 r-q q-p = 20 4 =5 which is an integer. So, the given series forms an AP . Infinite AP's are possible.

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