How do you find nth term rule for #a_2=28# and #a_5=-1792#?

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Answer 1 · 2016-08-17T22:33:51

#a_n = -7(-4)^(n-1)#

The difference between the number implies this is a GP.

#a_5 = ar^4 = -1792#
#a_2 = ar= 28#

Divide the terms: #a_5/a_2 = (ar^4)/(ar) = (-1792)/28#

#(cancelar^4)/(cancelar) = -64#

#r^3 = -64#

#r = -4#

#a_1 = 28/(-4) = -7#

#:. a_n = -7(-4)^(n=1)#