**The 7th term of the series 6, 12, 24, ... is?**

To find the 7th term of the given series, we need to determine the pattern or rule that governs the sequence. By analyzing the terms, we can observe that each term is obtained by doubling the previous term. Let's break down the series to understand it better:

1st term: 6
2nd term: 12 (6 x 2)
3rd term: 24 (12 x 2)

We can see that each term is obtained by multiplying the previous term by 2. Therefore, we can establish the pattern as follows:

**Pattern: Each term is obtained by multiplying the previous term by 2.**

Now that we have established the pattern, we can find the 7th term using the formula for the nth term of a geometric sequence. The formula is given as:

**nth term = a * r^(n-1)**

where:
- a is the first term of the sequence
- r is the common ratio (2 in this case)
- n is the position of the term we want to find (7th term in this case)

Let's substitute the values into the formula to find the 7th term:

**a = 6 (first term)**
**r = 2 (common ratio)**
**n = 7 (position of the term)**

**7th term = 6 * 2^(7-1)**
**7th term = 6 * 2^6**
**7th term = 6 * 64**
**7th term = 384**

Therefore, the 7th term of the series 6, 12, 24, ... is 384.

In summary:
- The given series follows a pattern where each term is obtained by doubling the previous term.
- Using the formula for the nth term of a geometric sequence, we can find the 7th term.
- By substituting the values into the formula, we find that the 7th term is 384.

The 7th term is 384