Respuesta :

We need to find the n term formula:

The given sequence represents an arithmetic sequence and it follows the next form:

[tex]a_n=a+(n-1)d[/tex]

Where a represents the first term, in this case, a= -31

n is the term of the sequence

And d is the constant:

Let's find the constant

a1 to a2 =

-32 to -132, then, -32 needs -100 units bo equal to -132.

Now, -132 need -100 units to be equal to -232.

-232 needs -100 units to be equal to -332

Therefore, the constant d is equal to -100, d=-100

Replacing these values:

[tex]a_n=-32+(n-1)(-100)[/tex]

Then:

[tex]a_n=-32-(n-1)(100)[/tex]

With this n formula, we can replace n=40, then, we will find a40:

[tex]a_{40}=-32-(40-1)100[/tex]

Therefore:

[tex]a_{40}=-3932[/tex]