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 \(T_{n}=a\times 10^{n-1}\)
Where a = first term = 0.006
r = common ratio = \(\frac{0.006\times 10}{0.006}\) = 10
n = Number of the term
So the explicit formula will be \(T_{n}=(0.006)\times 10^{n-1}\)
Now we have to get 5th and 6th term.
\(T_{5}=(0.006)\times 10^{5-1}\)
=\(0.006\times 10^{(5-1)}\)
=\(0.006\times 10^{(4)}\)
= 60
\(T_{6}=(0.006)\times 10^{6-1}\)
= \(0.006\times 10^{5}\)
= \(0.006\times 100000\)
= 600
Therefore, 5th and 6th terms will be 60 and 600.
