The sixth term is -243/2048 ⇒ answer B
Step-by-step explanation:
* Lets explain the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)
# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5) Â
* General term (nth term) of a Geometric sequence:
# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4
# Un = ar^(n-1), where a is the first term , r is the constant ratio
 between each two consecutive terms  and n is the position of the
 number in the sequence
- Ex: U5 = ar^4 Â , Â U7 = ar^6 Â , Â U10 = ar^9 Â , Â U12 = ar^11
- Lets solve the problem
∵ The sequence is 1/2 , -3/8 , 9/32
- Lets find the constant ratio r
∵ The first term is a = 1/2
∵ The second term is U2 = ar
∵ The second term  U2 = -3/8
∴ ar = -3/8
∴ 1/2 r = -3/8 ⇒ multiply both sides by 2
∴ r = -3/4
- Lets find the sixth term
∵ a = 1/2 and r = -3/4
∵ n = 6
∴ U6 = ar^5
∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048
* The sixth term is -243/2048