Question

What is the relationship between the terms in the pattern? 0.006, 0.06, 0.6, 6

Answer 1

they're going up by tenths

Answer 2

Each term is the previous one multiplied by 10

In math notation:

`a_n=10(a_(n-1))`

Explanation:

Notice if we multiply the first term by 10 we get the second:

0.006*10 = 0.06

Similarly the second term by 10 yields to the third term:

0.06*10 = 0.6

And the third term by 10 yields to the last term in the pattern:

0.6*10 = 6

If we call the n-th term
`a_n`

Then notice it is got by multiplying it by the previous term
`a_(n-1)]`

So:
`a_n=10(a_(n-1))`