When attempting to describe sequences, it is often convenient to look at first differences. Here, they are 4, 6, 8, 10, each obviously 2 more than the next.
a) Second differences are 2.
b) The next three numbers will be
.. 30+12 = 42
.. 42+14 = 56
.. 56+16 = 72
c) There are a number of ways to write an equation for this. One of the simpler ones is to let a graphing calculator perform quadratic regression and tell you the equation.
.. a[n] = n(n +1)
d) 117 is not in the sequence. The sequence consists only of even numbers, of which 117 is not one.
e) 10100 is in the sequence. It is 100*101, hence the 100th term of the sequence.