Question

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

Answer 1

∴ So the answers are
`a_(2) =-(91)/(19)` ,
`a_(3) =-(531)/(91)` and
`a_(4) =-(3019)/(531)`

Explanation:

Given,

`a_(1) =19` and

`a_(n) =(4)/(a_(n-1) )-5` (equation 1)

plug
`n=2` in equation 1;

`a_(2) =(4)/(a_(2-1) )-5`

`a_(2) =(4)/(a_(1) )-5`

Plug
`a_(1)` value in above equation;

`a_(2) =(4)/(19)-5`

`a_(2) =-(91)/(19)`

Similarly,

plug
`n=3` in equation 1;

`a_(3) =(4)/(a_(3-1) )-5`

`a_(3) =(4)/(a_(2) )-5`

Plug
`a_(2)` value in above equation;

`a_(3) =(4)/(-(91)/(19) )-5`

`a_(3) =-(531)/(91)`

And,

plug
`n=4` in equation 1;

`a_(4) =(4)/(a_(4-1) )-5`

`a_(4) =(4)/(a_(3) )-5`

Plug
`a_(3)` value in above equation;

`a_(4) =(4)/(-(531)/(91) )-5`

`a_(4) =-(3019)/(531)`

∴ So the answer are
`a_(2) =-(91)/(19)` ,
`a_(3) =-(531)/(91)` and
`a_(4) =-(3019)/(531)`