How do you find these missing terms [__,8,__,128,....]?

1 Answer
Jun 6, 2016

Answer:

There are two solutions:

#4# and #32#

Or:

#-4# and #-32#

Explanation:

If the general term of the sequence is #a_n# (#n = 1, 2, 3,...#) then we can rephrase the problem like this:

A geometric sequence has #a_2 = 8# and #a_4 = 128#. What are #a_1# and #a_3# ?

The general term of a geometric sequence is described by the formula:

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

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

In our example, we find:

#r^2 = (a r^3)/(a r) = a_4/a_2 = 128/8 = 16 = 4^2#

So #r = +-4#.

If #r = 4# then:

#a_1 = a_2/r = 8/4 = 2# and #a_3 = a_2*r = 8*4 = 32#

If #r = -4# then:

#a_1 = a_2/r = 8/(-4) = -2# and #a_3 = a_2*r = 8*(-4) = -32#