Odpowiedź:
[tex]a_{n}[/tex] = - n + 14
Szczegółowe wyjaśnienie:
[tex]a_{2} +a_{5}-a_{3} = 10[/tex] [tex]a_{2} + a_{9} =17[/tex]
[tex]a_{1}[/tex] + r + [tex]a_{1}[/tex] + 4r - ( [tex]a_{1}[/tex] + 2r ) = 10 [tex]a_{1}[/tex] + r + [tex]a_{1}[/tex] + 8r = 17
[tex]a_{1}[/tex] + 3r = 10 2[tex]a_{1}[/tex] + 9r = 17
[tex]a_{1}[/tex] = 10 - 3r [tex]2*(10 - 3r) + 9r = 17[/tex]
20 - 6r + 9r = 17
3r = 17 - 20
3r = - 3 /: 3
r = - 1
[tex]a_{1}[/tex] = 10 - 3 * ( - 1 ) = 10 + 3 = 13
[tex]a_{n}= a_{1} +(n-1)*r[/tex]
[tex]a_{n}= 13 +(n-1)*(-1)[/tex] = 13 - n + 1 = - n + 14
