a) To determine the common ratio, we would divide a term by its previous term. Looking at the given sequence,
common ratio, r = 1920/7680 = 480/1920 = 0.25
b) This is a geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
Tn represents the value of the nth term
a represents the value of the first term
n represents the number of terms
r represents the common ratio
Looking at the given sequence,
a = 7680
r = 0.25
The equation to represent the sequence is
Tn = 7680(0.25)^(n - 1)
c) To find the 6th term, T6, n = 6
Therefore,
T6 = 7680(0.25)^(6 - 1) = 7680(0.25)^5
T6 = 7.5
The 6th term is 7.5