Final answer:
To find the next terms in the exponential sequence, divide any term by its preceding term to find the common ratio. Then multiply the previous term by the common ratio to find the next term.
Step-by-step explanation:
To find the next three terms in the exponential sequence, we need to determine the common ratio. The common ratio is found by dividing any term in the sequence by its preceding term. In this case, we divide 6 by 18: 6/18 = 1/3.
So, the common ratio is 1/3. To find the third term, we multiply the second term (6) by the common ratio: 6 * 1/3 = 2.
Similarly, to find the fourth term, we multiply the third term (2) by the common ratio: 2 * 1/3 = 2/3. And to find the fifth term, we multiply the fourth term (2/3) by the common ratio: 2/3 * 1/3 = 2/9.
Therefore, the next three terms in the exponential sequence are 2, 2/3, and 2/9.