Question

÷a₁,a₂,a₃,a₄,.... a₃=5 a₆=11 a₈=?

Answer 1

$\displaystylr a_3=5,~a_6=11,~a_8=?\\a_3=5 \Rightarrow a_{3-1}+r=5 \Rightarrow a_2+r=5 \Rightarrow a_1+2r=5 \Rightarrow a_1=5-2r \\ a_6=11 \Rightarrow a_{6-1}+r=11 \Rightarrow a_5+r=11 \Rightarrow a_1+5r=11 \Rightarrow \\ \Rightarrow 5-2r+5r=11 \Rightarrow 5+3r=11 \Rightarrow 3r=11-5 \Rightarrow 3r=6 \Rightarrow\\ \Rightarrow r=\frac{6}{3} \Rightarrow r=2 \\ a_1=5-2r \Rightarrow a_1=5-2\cdot2\Rightarrow a_1=5-4 \Rightarrow a_1=1$
$\displaystyle a_8=a_{8-1}+r \Rightarrow a_8=a_7+r \Rightarrow a_8=a_1+7r \Rightarrow a_8=1+7 \cdot 2 \Rightarrow \\ \Rightarrow a_8=1+14 \Rightarrow \boxed{a_8=15 }$