Question

write the rule for the following arithmetic sequence:


14, 9, 4, -1,...

Answer 1

$a_1=14;\ a_2=9;\ a_3=4;\ a_4=-1\\\\d=a_2-a_1=a_3-a_2=a_4-a_3\\\\d=9-14=-5\\d=4-9=-5\\d=-1-4=-5\\\\a_n=a_1+(n-1)d\\\\a_n=14+(n-1)\cdot(-5)=14-5n+5=19-5n\\\\ \left\{\begin{array}{ccc}a_1=14\\a_{n}=a_{n-1}-5\end{array}\right$