Question

The number below follows a pattern. .006 .06 0.6 6 what are the next two numbers in the pattern

Answer 1

60 and 600 are the next 2 numbers

Answer 2

5th and 6th terms will be 60 and 600.

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* 10^(n-1)`

Where a = first term = 0.006

r = common ratio =
`(0.006* 10)/(0.006)` = 10

n = Number of the term

So the explicit formula will be
`T_(n)=(0.006)* 10^(n-1)`

Now we have to get 5th and 6th term.

`T_(5)=(0.006)* 10^(5-1)`

=
`0.006* 10^((5-1))`

=
`0.006* 10^((4))`

= 60

`T_(6)=(0.006)* 10^(6-1)`

=
`0.006* 10^(5)`

=
`0.006* 100000`

= 600

Therefore, 5th and 6th terms will be 60 and 600.