How do you find the indicated term of the geometric sequence where #a_6=3#, r=2, n=12?

1 Answer
Alan P.
Jun 22, 2017

#a_12=color(red)(192)#

Explanation:

#a_6=3=a_5xxr=a_5xx2#
#color(white)("XXX") rarr 3=a_5xx2#
#color(white)("XXX") rarr a_5=3/2#

Similarly
#color(white)("XXX")a_4=3/(2^2)#
#color(white)("XXX")a_3=3/(2^3)#
#color(white)("XXX")a_2=3/(2^4)#
#color(white)("XXX")a_1=3/(2^5)#
#color(white)("XXX")a_0=3/(2^6)#

#a_n=a_0xxr^n#
#color(white)("XXX")rarr a_12=3/(2^6)xx2^12#
#color(white)("XXXXXX")=3xx2^6#
#color(white)("XXXXXX")=2xx64#
#color(white)("XXXXXX")=192#

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