Divide any term in the sequence by the previous term. That is the common ratio of a geometric series.
If the series is defined in the form of a recurrence relationship, it is even simpler.
For a geometric series with common ratio r, the recurrence relation is
Un+1 = r*Un for n = 1, 2, 3, ...
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Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.
The 99th term would be a times r to the 98th power ,where a is the first term and r is the common ratio of the terms.
1/8
It is 4374