Final answer:
The general term (a_n) of the geometric sequence is a_n = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio. Then, a₇, the seventh term of the sequence, can be found using this formula.
Step-by-step explanation:
In a geometric sequence, each term is obtained by multiplying the preceding term by a fixed number called the common ratio.
Given the sequence: 1.2, 2, 4, 4.8, 9.6
We notice that each term is obtained by multiplying the previous term by a constant factor. To find the common ratio (r), we can divide any term by its preceding term. Let's take the ratio of the 4th term to the 3rd term: 4.8 / 4 = 1.2. Hence, the common ratio is 1.2.
The first term (a₁) is 1.2, and the common ratio (r) is also 1.2. Therefore, the general term of the sequence (a_n) can be written as a_n = 1.2 * 1.2^(n-1).
Now, to find the seventh term (a₇), substitute n = 7 into the formula:
a₇ = 1.2 * 1.2^(7-1) = 1.2 * 1.2^6 = 1.2 * 9.1776 ≈ 11.01312.
Thus, the seventh term of the sequence is approximately 11.01312.