What is the natural number x if 1+ 5 + 9 + ...+ x = 231?

The series in this question is called a arithmetic
sequence. The difference between each number is 4

The first
number is 1, the last number is X, there are (x-1)/4 +1 terms in the sequence (you can
verify that using a lot of ways)

then the total sum
is

((1+X)*（（x-1)/4+1))/2
=231

(x^2-1)/4 +1+X=462   (multiplication Property of
Equality(P.O.E))

x^2 +3 +4X = 1848 ( Addition and
Multiplication P.O.E)

X^2 +4X - 1845 =0
(Simplify)

(x+45)(x-41) = 0
 (Factoring)

x= -45 or 41 Eliminate the negative
root

The Term is 41