Multiple choice general knowledge math & puzzles

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

  1. -2

  2. -4

  3. -12

  4. 8
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C Correct answer
Explanation

Let terms be a, ar, ar^2, ar^3. a(1+r)=12 and ar^2(1+r)=48. Dividing gives r^2=4, so r=2 or -2. Since terms alternate signs, r must be -2. Then a(1-2)=12 => -a=12 => a=-12.

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