Final answer:
To find the value of the seventh term in a geometric sequence, divide the ninth term by the third term to find the common ratio. Then, multiply the third term by the common ratio raised to the power of 4 to find the seventh term.
Step-by-step explanation:
To find the value of the seventh term in a geometric sequence, we need to find the common ratio of the sequence first. We can do this by dividing any term by the previous term. In this case, we can divide the ninth term (13/9) by the third term (1053) to get the common ratio: (13/9)/(1053) = 13/9 * 1/1053 = 13/9537. Now that we have the common ratio, we can find the seventh term by multiplying the third term (1053) by the common ratio raised to the power of 4 (since the seventh term is two terms after the third term): 1053 * (13/9537)^4 = 922.00.