Suppose that we have the following sequence :
a_1=1
a_n=1/2 a_(n-1) , for n> 1
we define a new sequence as such :
b_1=a_1
b_n=b_(n-1)+a_n
find the 50th term of the sequence b_n.
find the 1th term of the sequence b_n.

We have 
which is the first term in the sequence
where  is the term in the sequence

which is the first term in the  sequence


term of 




- we work this out from the first term 
- we work this out from the first term 


Hence 

The  term is 



from 


Hence,

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