Question

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

a. i; 1, i, -1

c. -i; -1,- i, 1

b. i; -1, -i, 1

d. -i; 1, i, -1

Please select the best answer from the choices provided
A
B
C
D

Answer 1

Option A is correct.

Explanation:

Common Ratio of Geometric series is obtained by dividing by each next term of the series to its previous term

here in the problem two consecutive terms are -1 and -i

so dividing -i by -1 in order to find common ratio

r =
`(-i)/(-1) = i`

Since here common ratio is i

next 3 terms are given by

`T_4= rT_3\\T_4= (i)((-i) = -i^2=-(-1) = 1\\T_5 =rT_4= (i) (1)= i \\T_6= rT_5 = (i)(i) = i^2= -1 \\`

Therefore common ratio is i and next three terms are 1,i and -1

Therefore option A is correct .