Whats the missing term in the geometric sequence 25, __, 225?

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Answer 1 · 2015-11-13T16:51:32

Depending on the common ratio (#r = +-3#), either #A_2 = 75# or #A_2 = -75#.

#A_1 = 25#

#A_3 = 225#

#A_n = A_1r^(n - 1)#

#=> A_3 = A_1r^(3 - 1)#

#=> 225 = 25r^2#

#=> 9 = r^2#

#=> r = -3, r = 3#

If #r = -3#

#A_2 = 25(-3)^(2-1)#

#=> A_2 = 25(-3)#

#=> A_2 = -75#

If #r = 3#

#A_2 = 25(3)^(2-1)#
#=> A_2 = 25(3)#

#=> A_2 = 75#