Question

`20, 10, 2.5` ?

Answer 1

See explanation...

Explanation:

It is not clear what this question is asking.

Some possibilities:

`color(white)()`
What is the next number in the sequence `20, 10, 2.5` ?

Note that `20/10 = 2` and `10/2.5 = 4`, so we could expect the next item in the sequence to be:

`2.5 / 6 = 0.41bar(6)`

or

`2.5 / 8 = 0.3125`

Since this does not fall into the category of any standard sequence, we could justify all kinds of continuations of the sequence.

`color(white)()`
What number is missing in the geometric sequence `20, 10, 2.5`?

Note that the sequence:

`20, 10, color(red)(5), 2.5`

would be a geometric sequence, with each term being half of the preceding one.

`color(white)()`
What is the rule and next term of the sequence `20, 10, 5, 2.5`?

Note this assumes that `5` was missed from the question.

If so, then this looks like a geometric sequence with initial term `20` and common ratio `1/2`

The formula for a general term would be:

`a_n = 20*(1/2)^(n-1)`

and the next term of the sequence would be:

`2.5*(1/2) = 1.25`