Multiple choice

The sum of four numbers in G.P is 60 and the A.M of the 1st and the last is 18. The numbers are

  1. 4, 8, 16, 32

  2. 4, 16, 8, 32

  3. 16, 8, 4, 20

  4. None of these
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A Correct answer
Explanation

Let the GP be a, ar, ar^2, ar^3. Given a(1+r+r^2+r^3) = 60 and (a+ar^3)/2 = 18, so a+ar^3 = 36. Dividing the sum equation by this gives (1+r+r^2+r^3)/(1+r^3) = 5/3. This leads to 2r^3 - 3r^2 - 3r + 2 = 0, which has r = 2 as a solution. With r = 2, a(1+8) = 36 gives a = 4. The numbers are 4, 8, 16, 32.

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