Given series: 1, 2, 4...

To find the last term of the series, we need to determine the pattern or rule that governs the sequence. Looking at the given terms, we can observe that each term is obtained by multiplying the previous term by 2.

Pattern:
1st term: 1
2nd term: 2 (1 * 2)
3rd term: 4 (2 * 2)
4th term: 8 (4 * 2)
...

From the pattern, we can see that each term is obtained by multiplying the previous term by 2. Therefore, the nth term of the series can be expressed as 2^(n-1).

Finding the 10th term:
To find the 10th term, we substitute n = 10 into the formula:

10th term = 2^(10-1) = 2^9

Simplifying the expression:
2^9 = 512

Therefore, the 10th term of the series is 512.

Summary:
The given series is 1, 2, 4... and the pattern governing the sequence is multiplying each term by 2. By using this pattern, we can express the nth term of the series as 2^(n-1). Substituting n = 10, we find that the 10th term of the series is 512.