HELP fast please!!!!!Classify the sequence as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information. (12+(-8)+16/3+(-32/9)+64/27) Then, determine if the series is convergent or divergent.
Accepted Solution
A:
The sequence is geometric. The infinite series does converge.
Note how dividing any given term by the previous one leads to the same result -8/12 = -2/3 (16/3) divided by -8 = -2/3 and so on... So the common ratio is r = -2/3. This proves the sequence is geometric.
Since |r| < 1 is true, this means the infinite series converges to some fixed number.