#20, 10, 2.5# ?

1 Answer
Sep 13, 2016

Answer:

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#