**Finding the pattern**

To find the last term of the series 1, 2, 4, ..., we need to determine the pattern followed by the series. By observing the given terms, we can notice that each term is obtained by doubling the previous term. Let's break it down step by step.

**Step 1: Difference between terms**

To determine the pattern, let's find the difference between consecutive terms in the series:

2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
16 - 8 = 8

We can see that the difference between consecutive terms is increasing by a power of 2. It follows the pattern: 1, 2, 4, 8, ...

**Step 2: Finding the common ratio**

Now, let's find the common ratio between consecutive terms. We can do this by dividing a term by its previous term:

2 ÷ 1 = 2
4 ÷ 2 = 2
8 ÷ 4 = 2
16 ÷ 8 = 2

We can see that the common ratio between consecutive terms is 2.

**Step 3: General formula for the series**

Since the series follows a geometric progression (each term is obtained by multiplying the previous term by a constant ratio), we can use the general formula for the nth term of a geometric progression:

An = A1 * r^(n-1)

Where:
An = nth term of the series
A1 = first term of the series
r = common ratio
n = position of the term

**Step 4: Finding the last term**

We are given that the series has 7 terms. To find the last term, we can substitute the given values into the formula:

An = A1 * r^(n-1)
A7 = 1 * 2^(7-1)
A7 = 1 * 2^6
A7 = 1 * 64
A7 = 64

Therefore, the last term of the series 1, 2, 4, ..., up to 7 terms is 64.