Given that the third term #a_3# of a geometric sequence is #2# and the sixth term #a_6# is #128#, which term is #1/2# ?

1 Answer
Jul 26, 2016

Answer:

#a_2#

Explanation:

We can write the general term of a geometric sequence as:

#a_n = ar^(n-1)#

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

In our example #a_3 = ar^2# and #a_6=ar^5# so we find:

#r^3 = (ar^5)/(ar^2) = a_6/a_3 = 128/2 = 64 = 4^3#

So the only possible Real value of #r# is #root(3)(4^3) = 4#

Note that #1/2 = 2/4 = a_3/r#.

So #a_2 = 1/2#