Respuesta :
we are given the following sequence:
[tex]_{}29,,,,539,1083[/tex]To go from 539 to 1083 we multiply 539 by 2 and add 5, like this:
[tex]1083=539\times2+5[/tex]Therefore, for a number in position "n", the formula for its value is:
[tex]a_n=2a_{n-1}+5[/tex]Solving we get:
[tex]a_{n-1}=\frac{a_n-5}{2}[/tex]Replacing the current value for 539 we get:
[tex]a_5=\frac{a_6-5}{2}[/tex][tex]a_5=\frac{539-5}{2}=267[/tex]Now to find the 4th value:
[tex]a_4=\frac{a_5-5}{2}[/tex]Replacing:
[tex]a_4=\frac{267-5}{2}=131[/tex]For the third value:
[tex]a_3=\frac{a_4-5}{2}[/tex]Replacing:
[tex]a_3=\frac{131-5}{2}=63[/tex]The second value is already given as 29, therefore, the first value is:
[tex]a_1=\frac{a_2-5}{2}[/tex]Replacing:
[tex]a_1=\frac{29-5}{2}=12[/tex]Therefore, the sequence is:
[tex]12,29,63,131,267,539,1083[/tex]
