Introduction:

The given series is 1, 2, 4... and we need to find the last term of this series when there are 10 terms.

Explanation:

To find the last term of the series, we need to identify the pattern or rule that is followed in generating the terms.

Pattern of the series:

By observing the given series, we can see that each term is obtained by multiplying the previous term by 2.

1 * 2 = 2
2 * 2 = 4
4 * 2 = 8
...

So, the pattern of the series is that each term is obtained by multiplying the previous term by 2.

Finding the 10th term:

To find the 10th term of the series, we can use the formula for the nth term of a geometric sequence:

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

Where:
- nth term is the term we want to find
- a is the first term of the series
- r is the common ratio (in this case, 2)
- n is the position of the term in the series

In our case, the first term (a) is 1, the common ratio (r) is 2, and we want to find the 10th term (n = 10).

Using the formula, we can calculate the 10th term:

10th term = 1 * 2^(10-1)
= 1 * 2^9
= 1 * 512
= 512

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

Conclusion:

The last term of the series 1, 2, 4... when there are 10 terms is 512.