Answer:
The nth term will be:
Step-by-step explanation:
Given the sequence
-5, -15, -25, ...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]-15-\left(-5\right)=-10,\:\quad \:-25-\left(-15\right)=-10[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=-10[/tex]
The first element of the sequence is:
[tex]a_1=-5[/tex]
Thus, the nth term will be:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting the values [tex]d=-10[/tex]; [tex]a_1=-5[/tex]
[tex]a_n=-10\left(n-1\right)-5[/tex]
[tex]a_n=-10n+5[/tex]
Plug in n = 93 to determine the nth term
[tex]a_{93}=-10\left(93\right)+5[/tex]
[tex]a_{93}=-930+5[/tex]
[tex]a_{93}=-925[/tex]
Therefore, the nth term will be:
