Zad. 15
[tex]a_n=n^2-n\\a_{n+1}=(n+1)^2-(n+1)=n^2+2n+1-n-1=n^2+n\\\\a_{n+1}-a_n=r\\r=n^2+n-(n^2-n)=n^2+n-n^2+n=2n\\\\\text{Odp.} A, 3[/tex]
Zad. 16
[tex]\left \{ {{a_1=-2} \atop {a_{n+1}=n*a_n+4}} \right. \\a_2=a_{1+1}=1*a_1+4=-2+4=2\\a_3=a_{2+1}=2*a_2+4=2*2+4=4+4=8\\a_4=a_{3+1}=3*a_3+4=3*8+4=28\\\\S=-2+2+8+28=8+28=36\\\\\text{Odp. 36}[/tex]
Zad. 17
[tex]a_1=-2\frac12\\a_2=log_2x\\a_3=2log_2(x+2)+\frac12\\\\a_2=\frac{a_1+a_3}2\\log_2x=\frac{-\frac52+2log_2(x+2)+\frac12}2\\log_2x=\frac{-2+2log_2(x+2)}2\\log_2x=\frac{2(-1+log_2(x+2))}2\\log_2x=-1+log_2(x+2)\\log_2x-log_2(x+2)=-1\\log_2(\frac{x}{x+2})=-1\\2^{-1}=\frac{x}{x+2}\\\frac12=\frac{x}{x+2}\\\\x+2=2x\\2=2x-x\\\underline{2=x}\\\\[/tex]
Zad. 18
[tex]a_{12}=30\\S_{12}=162\\162=\frac{a_1+30}2*12\\162=(a_1+30)*6 /:6\\27=a_1+30 /-30\\\underline{a_1=-3}[/tex]
