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]
