Question

A3=11 a11=3 calculati a7

Answer 1

$\displaystyle a_3=11,~ a_{11}=3,~a_7=? \\ a_3=11 \Rightarrow a_{3-1}+r=11 \Rightarrow a_2+r=11 \Rightarrow a_1+2r=11 \Rightarrow \\ \Rightarrow a_1=11-2r \\ a_{11}=3 \Rightarrow a_{11-1}+r=3 \Rightarrow a_{10}+r=3 \Rightarrow a_1+10r=3 \Rightarrow \\ \Rightarrow 11-2r+10r=3 \Rightarrow -2r+10r=3-11 \Rightarrow 8r=-8 \Rightarrow r=-1 \\ a_1=11-2r \Rightarrow a_1=11-2 \cdot (-1) \Rightarrow a_1=11+2 \Rightarrow a_1=13 \\ a_7=a_{7-1}+r=a_6+r=a_1+6r=13+6 \cdot (-1)= 13-6= 7 \\ \boxed{a_7=7}$