[tex]13 , 19 , 26 , 34 , 43 , .....[/tex]

Step-by-step explanation:

Concept:

The nth element of this sequence can be represented by the below expression as :

[tex]a(n)=\frac{n(n+3)}{2} -1[/tex]

Given :

The sequence [tex]13 , 19 , 26 , 34 , 43 , ....[/tex]

Find :

The [tex]93[/tex]rd number in the given sequence.

Solution:

Let us use the expression [tex]a(n)=\frac{n(n+3)}{2} -1[/tex] and use [tex]n=93[/tex] to get:

[tex]a(93)=\frac{93(93+3)}{2} -1\\=\frac{8928}{2} -1\\=4464-1\\=4463[/tex]

Thus, the [tex]93[/tex]rd number in the sequence is [tex]4463[/tex].