1.For the geometric sequence: 3,9,27,81.... a.Find the nth term? b.the 18th term? 2. The ñ term of geometric sequence is 2 (4n-1)find the 3rd term. Thanks gus for you cooprative

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Answer 1 · 2017-11-02T17:35:56

see below

a GP has terms

#a, ar,ar^2,ar^3,...ar^(n-1),....#

#(a): 3,9,27,81...#

for this series

#a=3#

#r=u_(n+1)/u_n#

#r=9/3=3#

a quick mental check will see that is true for other adjacent terms

#:."nth term"=3*3^(n-1)=3^n#

#(b)#

#18th" term "=3*3^(18-1)=3*3^17=3^18#

#(c)#

now as it is written

nth term=2(4n-1) doesn't give a GP
because

#1st=2(4xx1-1)=2xx3=6#

#2nd=2(4xx2-1)=2xx7=14#

#3rd=2(4xx3-1)=2xx11=22#

check for common ratio

#u_3/u_2=22/14=11/7#

#u_2/u_1=14/6=7/3#

not the same so not a GP.

if #2^(4n-1) #was meant

then the third term would be

#2^(4xx3-1)=2^11#