The sum to infinity of a convergent geometric series is , and the second term is . What are the possible values of the common ratio ?

Answer and explanation

Correct answer: D. or

.
.
.
Both values satisfy the convergence condition .
  1. Step 1: Relate the first term and common ratio using the sum to infinity formula :
  2. Step 2: Use the second term condition to form an equation for :
  3. Step 3: Factor the quadratic equation :
Answer
or .

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