Question

The first four terms of a GP is 81, 27,9,3
The sum to infinity of this GP is:

Answer 1

We can see this is a decreasing progression which means we can sum this up . The common ratio here is 1/3 which means the next few terms are 1 , 1/3 , 1/9 , 1/27 and so on . We know the sum of 1/3 + 1/9 + 1/27 + ... till infinity is 0.5 . Therefore the sum of this whole series is just 121.5 .

In case you don't know how i got 1/3 + 1/9 + 1/27 + .... as 0.5 comment below i will try to explain . (✿◠‿◠)

Answer 2

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81= 3*3*3*3

27=3*3*3

9=3*3

3= Well just 3

1=3^0

Next we see that the series progresses to 1/3 I.e 3 raised to a negative indices of 1 or simply 3^-1.. So by this the next one on the series is 3^-2. Which is 1/9 thus the 7th term is 1/9.