Find out the missing term of the number series given below.

68, ?, 407, 470, 496, 503

The correct option is 283.

To find the missing term in the given number series, let us observe the differences between consecutive terms starting from the right side of the series:

$503-496=7$

$496-470=26$

$470-407=63$

Notice that each difference can be written in the form of $n^3-1$:

$7=2^3-1=8-1$

$26=3^3-1=27-1$

$63=4^3-1=64-1$

Continuing this pattern backwards, the differences to add starting from 68 should follow $n^3-1$ for $n=6$ and $n=5$:

For $n=6$:
$6^3-1=216-1=215$

For $n=5$:
$5^3-1=125-1=124$

Now, calculate the missing term by adding 215 to the first number (68):

$\text{Missing Term}=68+215=283$

We can verify this result by adding the next difference (124) to 283:

$283+124=407$

This matches the next term in the series (407). Therefore, the missing term is 283.