Question 1164214
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The statement of the problem is faulty....<br>
We are told that the first terms of the AP and GP are the same; and we are told that the sum of those two terms is 3.  So the first term of each sequence is 3/2.<br>
We are told the common ratio for the GP is 2; so the first three terms of the GP are 3/2, 3, and 6.<br>
We are told the first three terms of the new sequence are 3, 7, and 11.<br>
That means the first three terms of the AP are 3-3/2 = 3/2, 7-3 = 4, and 11-6 = 5.<br>
But 3/2, 4, 5 is not an AP.<br>