Final answer:
To determine the eighth term (a8) of the geometric sequence, the common ratio is first calculated as 5 by dividing the second term by the first. Using the geometric sequence formula and the common ratio, a8 is calculated to be 468750.
Step-by-step explanation:
To find the eighth term (a8) of a geometric sequence, we use the formula a8 = a1 * r^7, where a1 is the first term and r is the common ratio of the sequence. The second term of the sequence is given as 30 and the first term is 6, so the common ratio r can be calculated by dividing the second term by the first term: r = 30 / 6 = 5. Now, we substitute the values into the formula:
a8 = 6 * 5^7
Calculating this, we find that:
a8 = 6 * 78125
a8 = 468750
Therefore, the eighth term of the geometric sequence is 468750.