Question

Sequence Problem Below

Answer 1

`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}`

Explanation:

`\displaystyle\large \boldsymbol{Rule: t_n=S_(n)-S_(n-1)} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_(n-1)=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_(n)-S_(n-1)=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_(1)=1-5=-4`