What is the common ratio of the sequence #\frac { 3} { 100} ,\frac { 3} { 50} ,\frac { 3} { 25} ,\frac { 3} { 12.5}#?

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Answer 1 · 2018-01-23T11:29:55

Common ratio of the sequence is #2#

Let #a_1 and r# be the first term and common ratio of the

sequence #{a_1 , a_1*r , a_1*r^2 , a_3*r^3} :. #

#a_1=3/100 , a_1*r=3/50, a_1*r^2=3/25 ,a_3*r^3=3/12.5#

Common ratio #r =(cancel(a_1)*r)/cancel(a_1)=(cancel(a_1)*r^cancel2)/(cancel(a_1)*cancelr)#

Common ratio #r =(3/50)-:(3/100)=cancel3/50*100/cancel3=2#.

Similarly #r =(3/25)-:(3/50)=cancel3/25*50/cancel3=2#.

Common ratio of the sequence is #r =2# [Ans]