[Math] How to find N in geometric sequence nor series if the given are only the last term and the ratio

geometric seriessequences-and-series

The question is: The last term of a geometric sequence is 625. If the common ratio is 1/3, how many terms does the sequence have?

Best Answer

the solution is not unique. since $$u_n=u_1 (1/3)^{n-1}=625$$

we can take

$$u_1=625 , n=1$$ or $$u_1=1875, n=2... $$