Question #39a8d

1 Answer
Mar 5, 2016

The answer is 108.

Explanation:

#x_2+x_4=104#
#x_2-x_4=40#

so, adding member to member the two equations:

#2x_2=144rArrx_2=72#

and

#x_4=72-40=32#.

The geometric sequence is a sequence in which the ratio between two consecutive numbers is constant (#=q#).

So:

#x_4=x_3*q=(x_2*q)*q=x_2*q^2#,

then:

#q^2=x_4/x_2=32/72=4/9rArrq=2/3#, (#q# is a positive number!)

and:

#x_2=x_1*qrArrx_1=x_2/q=72*3/2=108#.