Question

progresia aritmetuca (an) n>=1 are suma primilor 13 termeni 156 .Calcuati a6+a7+a8

Answer 1

$\it S_{13}=\dfrac{(a_1+a_{13})\cdot13}{2}=156 \Rightarrow a_1+a_{13}=156\cdot\dfrac{2}{13} \Rightarrow a_1+a_{13}=24 \Rightarrow \\ \\ \\ \Rightarrow a_7-6r+a_7+6r=24 \Rightarrow 2a_7=24 \Rightarrow a_7=12\\ \\ \\ a_6+a_7+a_8=a_7-r+a_7+a_7+r=3a_7=3\cdot12=36$