Question

is the sequence geometric? if so, identify the common ratio.

1/3,2/9,4/27,8/81,16/243,....

Answer 1

Yes, the sequence is geometric.

The second term divided by the first term is: \[2/9 \div 1/3 = 2/9 \times 3/1 = 2/3\]
The third term divided by the second term is: \[4/27 \div 2/9 = 4/27 \times 9/2 = 2/3\]
You can try the fourth term divided by the third term which will also be 2/3.

Therefore, the sequence is geometric and the common ratio is 2/3.