[tex]a_n=a_1+(n-1)*r\\\\1 a. \\a_1=100\\a_2=98\\a_2-a_1=r\\r = -2\\a_n=100+(n-1)*(-2)\\a_n=100-2n+2\\a_n=102-2n\\\\2=102-2n\\2-102=-2n\\-100=-2n\\n=50[/tex]
Odp. Wzor ogolny to an = 102-2n, 50 wyraz tego ciagu jest rowny 2.
[tex]2b. \\\\a_1 = -14\\a_2=-12\\-12=a_1+(2-1)*r\\-12=-14+1r\\-12+14=1r\\r=2\\\\a_n=-14+(n-1)*2\\a_n=-14+2n-2\\a_n=-16+2n\\\\2=-16+2n\\2+16=2n\\18=2n\\n=9[/tex]
Odp. Wzor ogolny to an = -16+2n, 9 wyraz tego ciagu jest rowny 2.
[tex]3c. \\a_1 = 9\frac12\\a_2 = 9\\9 = 9\frac12 + (2-1)*r\\9 = 9\frac12+r\\9-9\frac12=r\\-\frac12=r\\\\a_n=9\frac12+(n-1)*(-\frac12)\\a_n=9\frac12-\frac12n+\frac12\\a_n=10-\frac12n\\\\2 = 10-\frac12n\\2-10=-\frac12n\\-8=-\frac12n /*2\\-16=-n\\n=16[/tex]
Odp. Wzor ogolny to [tex]a_n=10-\frac12n[/tex], 16 wyraz tego ciagu jest rowny 2.
