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

1 Answer
Nov 13, 2015

Answer:

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

Explanation:

#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#