Answer:
the common ratio here is -3/2.
Step-by-step explanation:
Each term is r times the previous term. Find r. The general formula for a geometric sequence is a(n) = a(1)*r^(n - 1).
Then 3/4 = (-1/2)*r^(2 - 1), or 3/4 = (-1/2)*r^(1), so that 3/4 = (-1/2)r. Solving for r, we divide both sides by -1/2, obtaining:
(3/4)*(-2) = r = -3/2.
Check: If the first term is -1/2 and the common ratio is -3/2, find the second term:
a(2) = a(1)*(-3/2)^(2 - 1), or -1/2*(-3/2)^1, or a(2) = 3/4. This agrees with the 2nd term of the given sequence.
Find the 3rd term: a(3) = (-1/2)*(-3/2)^2 = (-1/2)(9/4 = -9/8. This agrees with the 3rd term of the given sequence.
Thus, we have confirmed that the common ratio here is -3/2.
