oblicz 7 wyraz ciagu a) an=2n+6 Wyznacz ciag arytmetyczny majac dane a) a2 =5 a3=7 b) a3=8 S6=57

Witaj. Zadanie 1. [latex]a_{n}=2n+6\\a_{7}=2cdot7+6=14+6=20[/latex] Zadanie 2. a) [latex]a_{2}=5\\a_{3}=7\\a_{2}+r=a_{3}\\r=a_{3}-a_{2}=7-5=2\\a_{1}+r=a_{2}\\a_{1}=a_{2}-r=5-2=3\\a_{n}=a_{1}+r(n-1)\\a_{n}=3+2(n-1)\\a_{n}=2n+1[/latex] b) [latex] left { {{a_{3}=8} atop {S_{6}=57}} ight. \\ left { {{a_{1}+2r=8} atop {frac{a_{1}+a_{6}}{2}cdot 6=57}} ight. \\ left { {{a_{1}+2r=8} atop {3(a_{1}+a_{1}+5r)=57}} ight. \\ left { {{a_{1}+2r=8} atop {2a_{1}+5r=19}} ight. \\ left { {{-2a_{1}-4r=-16} atop {2a_{1}+5r=19}} ight. \+-----\\r=3\\ left { {{a_{1}=2} atop {r=3}} ight. \\a_{n}=a_{1}+r(n-1)\\a_{n}=2+3(n-1)\\a_{n}=3n-1[/latex]