What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

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Answer 1 · 2017-01-04T00:37:25

#+-250#

The general term of a geometric sequence has the form:

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

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

In our example:

#a_1 = 1250" "# and #" "a_3 = 50#

So:

#r^2 = (ar^2)/(ar^0) = a_3/a_1 = 50/1250 = 1/25 = 1/5^2#

Hence:

#r = +-1/5#

Then:

#a_2 = a*r^(2-1) = 1250*(+-1/5) = +-250#