What are the next three terms in the sequence #12, 4, 3/4# ?

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Answer 1 · 2016-03-24T14:47:52

This looks like a geometric sequence with common ratio #1/3#, with an error in the third term, which should be #4/3# rather than #3/4#.

If so, then the next #3# terms are: #4/9#, #4/27#, #4/81#

With only three terms, about the only pattern which makes sense is if the third term should be #4/3# rather than #3/4#.

If this is so, then this is a geometric sequence with initial term #12# and common ratio #1/3#.

The terms of a geometric sequence are given by the formula:

#a_n = a r^(n-1)#

where #a# is the initial term and #r# the common ratio.

In our case, #a=12#, #r=1/3# and the general term is given by:

#a_n = 12 (1/3)^(n-1)#

So the sequence starts:

#12, 4, 4/3, 4/9, 4/27, 4/81,...#