Question

известно, что в арифметической прогрессии Sn=n+5, найдите аn

Answer 1

$\displaystyle\bf\\S_{n} =n+5\\\\S_{1} =a_{1} =1+5=6\\\\a_{1} =6\\\\S_{2} =2+5=7\\\\S_{2}=a_{1}+a_{2}\\\\a_{1}+a_{2}=7\\\\a_{2}=7-a_{1}=7-6=1\\\\a_{2}=a_{1}+d\\\\d=a_{2}-a_{1}=1-6=-5\\\\a_{n} =a_{1} +d\cdot(n-1)=6-5\cdot(n-1)=6-5n+5=11-5n\\\\a_{n} =11-5n$