Answer:
5th and 6th terms will be 60 and 600.
Step-by-step explanation:
The given pattern of the numbers is 0.006, 0.06, 0.6, 6......
We can rewrite the pattern as 0.006, (0.006×10), (0.006×10²), (0.006×10³),......
As we can see its a geometric sequence.
So the explicit formula of the pattern will be [tex]T_{n}=a\times 10^{n-1}[/tex]
Where a = first term = 0.006
r = common ratio = [tex]\frac{0.006\times 10}{0.006}[/tex] = 10
n = Number of the term
So the explicit formula will be [tex]T_{n}=(0.006)\times 10^{n-1}[/tex]
Now we have to get 5th and 6th term.
[tex]T_{5}=(0.006)\times 10^{5-1}[/tex]
=[tex]0.006\times 10^{(5-1)}[/tex]
=[tex]0.006\times 10^{(4)}[/tex]
= 60
[tex]T_{6}=(0.006)\times 10^{6-1}[/tex]
= [tex]0.006\times 10^{5}[/tex]
= [tex]0.006\times 100000[/tex]
= 600
Therefore, 5th and 6th terms will be 60 and 600.
