Answer: the next term. Is 5
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = 40/27
r = 40/9 ÷ 40/27 = 20/9 × 27/40 = 3/2
n = 4 because the next term is the 4th term
The 4th term, T4 is
T4 = 40/27 × (3/2)^(4 - 1)
T4 = 40/27 × (3/2)^3
T4 = 40/27 × 27/8
T4 = 40/8
T4 = 5
