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Eight arithmetic means A1, A2,..., A8 are inserted between the numbers 5 and 50. Which of the following statements is/are correct?

1. A1, A3, A7 are in geometric progression
2. A3 is the harmonic mean between A2 and A5
3. A1, A3, A5 are in geometric progression
4. The geometric mean of A4 and (A2 + 1) equals A3

Correct answer: A1, A3, A7 are in geometric progression

Solution

With d = 5: A1=10, A2=15, A3=20, A4=25, A5=30, A6=35, A7=40, A8=45. Check A1, A3, A7: 10, 20, 40 - ratio 2 each, so GP. Check A1, A3, A5: 10, 20, 30 - differences equal but ratio 20/10=2, 30/20=1.5, NOT a GP. So only option A is correct.

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