Question

Find the formula for an for the arithmetic sequence given a1=94 and a6=85

Answer 1

`\bf \begin{array}{cll} term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ a_1&94\\ a_2&94+d\\ a_3&94+d+d\\ a_4&94+d+d+d\\ a_5&94+d+d+d+d\\ a_6&94+d+d+d+d+d\\ &85 \end{array}\qquad \implies 85=94+5d \\\\\\ -9=5d\implies \boxed{-\cfrac{9}{5}=d}\\\\ -------------------------------`


`\bf n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ a_1=94\\ d=-(9)/(5) \end{cases} \\\\\\ a_n=94+(n-1)\left(-(9)/(5) \right)\implies a_n=94+\cfrac{9}{5}-\cfrac{9}{5}n \\\\\\ a_n=95(4)/(5)-\cfrac{9}{5}n`