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

60, ?, 63.6, 70.8, 99.6, 243.6

To find the missing term in the given series, let us first examine the differences between the consecutive known terms of the series:

60, ?, 63.6, 70.8, 99.6, 243.6

Let the terms be denoted as $T_1$, $T_2$, $T_3$, $T_4$, $T_5$, and $T_6$.

Let us calculate the differences between the latter terms:

Difference between the 4th and 3rd terms:
$T_4-T_3=70.8-63.6=7.2$

Difference between the 5th and 4th terms:
$T_5-T_4=99.6-70.8=28.8$

Difference between the 6th and 5th terms:
$T_6-T_5=243.6-99.6=144.0$

Now, let us analyze the pattern in these differences (7.2, 28.8, 144.0):

$\frac{28.8}{7.2}=4$
$\frac{144.0}{28.8}=5$

The ratio between consecutive differences is increasing by 1 each time. Following this logical pattern, the ratio of the difference before 7.2 should be 3, and the one before that should be 2.

Let us denote the difference between the terms as $d_n=T_{n+1}-T_n$. The differences are:

$d_4=28.8$
$d_3=7.2$ (since $d_4=d_3\times 4$)
$d_2=\frac{7.2}{3}=2.4$
$d_1=\frac{2.4}{2}=1.2$

Alternatively, we can express the difference $d_n$ as:
$d_n=1.2\times n!$

Using this pattern to find the missing term $T_2$:

$T_2=T_1+d_1=60+1.2=61.2$

Let us verify with the next term:

$T_3=T_2+d_2=61.2+2.4=63.6$

Since this perfectly matches the third term in the series, the missing term is 61.2.