help please, i get close to what the answer is supposed to be but a not getting it correct.

Answer:∴ So the answers are [tex]a_{2} =-\frac{91}{19}[/tex] , [tex]a_{3} =-\frac{531}{91}[/tex] and [tex]a_{4} =-\frac{3019}{531}[/tex]Step-by-step explanation:Given,[tex]a_{1} =19[/tex] and[tex]a_{n} =\frac{4}{a_{n-1} }-5[/tex] (equation 1)plug [tex]n=2[/tex] in equation 1;[tex]a_{2} =\frac{4}{a_{2-1} }-5[/tex][tex]a_{2} =\frac{4}{a_{1} }-5[/tex]Plug [tex]a_{1}[/tex] value in above equation;[tex]a_{2} =\frac{4}{19}-5[/tex][tex]a_{2} =-\frac{91}{19}[/tex]Similarly,plug [tex]n=3[/tex] in equation 1;[tex]a_{3} =\frac{4}{a_{3-1} }-5[/tex][tex]a_{3} =\frac{4}{a_{2} }-5[/tex]Plug [tex]a_{2}[/tex] value in above equation;[tex]a_{3} =\frac{4}{-\frac{91}{19} }-5[/tex][tex]a_{3} =-\frac{531}{91}[/tex]And,plug [tex]n=4[/tex] in equation 1;[tex]a_{4} =\frac{4}{a_{4-1} }-5[/tex][tex]a_{4} =\frac{4}{a_{3} }-5[/tex]Plug [tex]a_{3}[/tex] value in above equation;[tex]a_{4} =\frac{4}{-\frac{531}{91} }-5[/tex][tex]a_{4} =-\frac{3019}{531}[/tex]∴ So the answer are [tex]a_{2} =-\frac{91}{19}[/tex] , [tex]a_{3} =-\frac{531}{91}[/tex] and [tex]a_{4} =-\frac{3019}{531}[/tex]