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:

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

What are the next three terms in the sequence 12, 4, 3/412, 4, 3/4 ?