Answer:
32.4
Explanation:
This is a geometric progression
The formula for geometric progression Tₙ= arⁿ⁻¹
Where a = first term
r = common ratio
n = number of term
First we need to find the common ratio
Common ratio = Tₙ/Tₙ₋₁
Using the 3rd term
Common ratio = T₃ /T₃₋₁
Common ratio = T₃ /T₂
T₃ = 3.6
T₂ = 1.2
Common ratio = 3.6/1.2
Common ratio = 3
From the question, we are to find it's 5th term
The formula is already given as :
Tₙ= arⁿ⁻¹
here a = first term
r = common ratio
n = number of terms
Where
a = 0.4
r = 3
n = 5
Therefore,
T₅ = 0.4 × 3⁵⁻¹
T₅ = 0.4 × 3⁴
T₅= 0.4 × 81
T₅ = 32.4
The next number in the pattern is 32.4