Is the sequence geometric? If so, identify the common ratio. 1/4, 3/16, 9/64, 27/256, 81/1024
Yes, the sequence is geometric because each term is multiplied by the same common ratio to get the next term.
To find the common ratio, we can divide each term by the previous term:
3/16 ÷ 1/4 = 3/16 * 4/1 = 12/16 = 3/4
9/64 ÷ 3/16 = 9/64 * 16/3 = 144/192 = 3/4
27/256 ÷ 9/64 = 27/256 * 64/9 = 1728/2304 = 3/4
81/1024 ÷ 27/256 = 81/1024 * 256/27 = 20736/27648 = 3/4
Therefore, the common ratio is 3/4.