213, 218, 233, 278, 413, ?
Find the missing number in the following number series.

To find the missing number in the series, let us first calculate the differences between consecutive terms:
First term = 213
Second term = 218
Third term = 233
Fourth term = 278
Fifth term = 413

Let us find the differences:

$218-213=5$

$233-218=15$

$278-233=45$

$413-278=135$

Now, let us analyze the pattern in these differences:
5, 15, 45, 135

We can observe that each successive difference is multiplied by 3:

$5\times 3=15$

$15\times 3=45$

$45\times 3=135$

Following this pattern, the next difference in the series will be:

$135\times 3=405$

To find the missing number, we add this difference to the last given term (413):

$413+405=818$

Therefore, the correct missing number in the series is 818.