Let be the statement ' is a geometric sequence' and be the statement ''. Which of the following is correct? (Here , and are real numbers, and a geometric sequence means and for some real .)

Answer and explanation

Correct answer: A. is a sufficient but not a necessary condition for

  1. Step 1: If and , then and , so : .
  2. Step 2: But , , has while no ratio gives , so .
Answer
is a sufficient but not a necessary condition for .
Why not the others: When the condition forces but leaves free; such triples are not geometric, so does not imply .

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