If first term of a G.P. is #1024# and fourth term is #-16#, which of the following is seventh term?

Question

A. #2#
B. #-0.25#
C. #4#
D. #-8#

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Answer 1 · 2017-03-20T03:46:50

B. #-0.25#

GP,
#a_n =a_1r^(n-1)#

#a_4 = a_1 * r^ (4-1)#

#-16 = 1024 * r^3#

#-16/1024 = r^3#

#-1/64 = r^3#

#-1/4 = r#

therefore,
#a_7 = 1024 * (-1/4)^(7-1)#

#= 1024 * (-1/4)^6#

#= 4^5 * (-1/4)^6 = -1/4 = -0.25#