Question

Determine the common ratio and find the next three terms of the geometric sequence i, -1, -i

Answer 1

The common ratio of the given terms in the geometric sequence is that number which is the answer derived from dividing the second term by the first term and the third term by the second term. In this item, the value of r (common ratio) is as calculated below.

 In this item, we should be mindful that i = sqrt (-1). The ratio is,

    r = (√-1)(√-1)/(√-1) = -1 (√-1)/-1 = √-1 

For the next three terms,

   n₄ = (-1)(√-1) = -i
   n₅ = (-i)(√-1)) = 1
   n₆ = (1)(√-1) = i

Thus, the next three terms are -1, 1, and i, respectively.