Multiple choice

Three numbers are in A.P and their sum is 21. If 1 , 5 , 15 are added to them respectively, they form a G.P. The numbers are

  1. 5, 7, 9

  2. 9, 5, 7

  3. 7, 5, 9

  4. None of these
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A Correct answer
Explanation

Let the AP be (a-d), a, (a+d). Sum = 3a = 21, so a = 7. After adding 1, 5, 15 respectively: (8-d), 12, (22+d). For GP: 12^2 = (8-d)(22+d). Solving d^2 + 14d - 32 = 0 gives d = 2 or d = -16. For d = 2: numbers are 5, 7, 9. For d = -16: numbers are 23, 7, -9. Both work, but only 5, 7, 9 appears in the options.

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