Find the twentieth and the nth of the sequence 4,9,14,19,....

Before any calculus of  any term, we'll have to establish
if the sequence is an arithmetical progression or geometric
progression.

We notice that the difference between 2
consecutive terms is:

9-4 =
5

14-9 = 5

19-14 =
5

.................

So, the
sequence is an arithmetical progression where the first term a1 = 4 and the common
difference, d = 5.

We'll apply the formula of finding the
n-th term of the a.p.

an = a1 +
(n-1)*d

an = 4 +
(n-1)*5

Substituting n by the value 20, we
could calculate the 20th term of the a.p.

a20 = a1 +
(20-1)*5

a20 = 4 + 19*5

a20 =
4 + 95

a20 =
99