Multiple choice

Check if the series is an AP. Find the common difference $d$ and write three more terms of the the following series. $2, 4, 8, 16,....$

  1. Common difference: $2$ and Other three terms are: $32, 64, 128$
  2. Common difference: $4$ and Other three terms are: $24, 32, 40$
  3. Common difference: $8$ and Other three terms are: $20, 24, 28$

  4. None of these
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D Correct answer
Explanation

The series 2, 4, 8, 16 is a geometric progression (ratio 2), not an arithmetic progression (AP). Therefore, there is no common difference d.

AI explanation

The series is a geometric progression, not an arithmetic progression, because each term is multiplied by 2 rather than having a constant difference added. The differences between successive terms are 2, 4, and 8, proving no common difference exists. The next three terms are found by continuing to multiply by 2, giving 32, 64, and 128. Therefore, None of these is the correct choice.

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