We have here in this an arithmetic progression. We have that the common difference is d = -5. (If we add -5 to -4, we obtain the second term -9, and so on).
We have that the first term is -4.
Then, according to the equation for the arithmetic progressions, we have:
[tex]a_n=a_1+(n-1)d[/tex]Then, the equation to find the nth term is the one above.
The equation for this case is:
[tex]a_n=-4+(n-1)\cdot(-5)[/tex]For example, we have in the sequence that the fourth term is -19. Then:
[tex]a_4=-4+(4-1)\cdot(-5)\Rightarrow a_4=-4+(3)\cdot(-5)\Rightarrow a_4=-4-15\Rightarrow a_4=-19[/tex]Therefore, to find the 24th element of the arithmetic progression, we have:
[tex]a_{24}=-4+(24-1)\cdot(-5)\Rightarrow a_{24}=-4+(23)\cdot(-5)\Rightarrow a_{24}=-4-115_{}[/tex]Then, the 24th element is:
[tex]a_{24}=-119[/tex]