Final answer:
The common ratio of the geometric sequence 1/2, -1/4, 1/8, -1/16 is found by dividing the second term by the first term, resulting in a common ratio of -1/2.
Step-by-step explanation:
To find the common ratio of the given geometric sequence 1/2, -1/4, 1/8, -1/16, we need to divide any term in the sequence by the term that precedes it.
Let's find the ratio using the first two terms:
Common ratio (r) = Second Term ÷ First Term
= (-1/4) ÷ (1/2)
= (-1/4) × (2/1) (Multiplying by the reciprocal of 1/2)
= -1/2
So, the common ratio for the given sequence is -1/2.