[tex]a_1+a_2+a_3+a_4=2016\\S_4=2016\\2016=\frac{a_1+a_4}2*4\\2016=2(a_1+a_4) /:2\\1008=a_1+a_4\\1008=a_1+a_1+3r\\1008=2a_1+3r[/tex]
[tex]a_5+a_6+a_7+...+a_{12}=2016\\2016=\frac{a_5+a_{12}}2*8\\2016=4(a_5+a_{12}) /:4\\504=a_5+a_{12}\\504=a_1+4r+a_1+11r\\504=2a_1+15r[/tex]
[tex]\left \{ {{1008=2a_1+3r /*(-1)} \atop {504=2a_1+15r}} \right. \\+\left \{ {{-1008=-2a_1-3r} \atop {504=2a_1+15r}} \right. \\-1008+504=-3r+15r\\-504=12r /:12\\r=-42\\\\1008=2a_1-126 /+126\\1134=2a_1 /:2\\a_1=567\\[/tex]
[tex]\text{Pierwszy wyraz ciagu to 567 a roznica ciagu to -42}[/tex]
[tex]a_1+(n-1)*r > 0\\567+(n-1)*(-42) > 0\\567-42n+42 > 0\\609-42n > 0 /+42n\\609 > 42n\\42n < 609 /:42\\n < 14.5\\\\a_{14}=a_1+13r\\a_{14}=567+13*(-42)\\a_{14}=567-546\\a_{14}=21\\\text{Najmniejszy dodatni wyraz tego ciagu to 14 wyraz, ktory wynosi 21}[/tex]
