which term of the G.P. 2,1,1/2,1/4... is 1/128?

t_n=a*r^n-1
where, a=initial term=2
n=nth term
r=common ratio=1/2
1/128=2*(1/256)=2*(1/2)⁸=2*(1/2)^n-1
Hence,n-1=8; …........n=9th term
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You can do this simply by putting 1/128 as an exponential term in terms of (1/2) which is the common ratio. The first terrm is a=2, d=1/2, so you can either equate them directly equal to the nth term expression to the value of n
OR you can substitute and do it in the other fashion.
nth term= a*r^n-1=2*(1/2)^(n-1)=1/128

1/128=1/2^7

So you can the value of n now...

Of course we can have alternative ways to do it and I have given the answer which is one of them …....



Good luck for your exams!!!!!!!!!
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