Question

Wyznacz ciąg arytmetyczny wiedząc że a6=5 i 1/3 i a9 =2

Answer 1

A2=a1+r
a6=a1+5r
5 i 1/3=a1+5r
a1=5r-5 i 1/3
3r = a9 - a6
3r =2-5 i 1/3
3r=-3 i 1/3
r=-10/9
2=a1+8*(-10/9) ,   18=a1-80 ,a1=98

a9=a1+8r
2=13r-5 i 1/3
7 i 1/3=13 r
22/3=13r  ,     22/3 *1/13=r ,   22/39=r
2=a1 + 176/39
2=a1+4 i 20/39
a1=-2 i 20/39
an=-2 i 20/39+ (n-1)*22/39