Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 38

$a_n= \dfrac{-2}{5}n+\dfrac{12}{5}$

We know that the general formula of an arithmetic sequence is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have $a_{11}-a_6=5d$ $-2=5d \implies d=\dfrac{-2}{5}$ Equation (1) gives: $a_n= \dfrac{-2}{5}n+\dfrac{12}{5}$ Thus: $a_n= \dfrac{-2}{5}n+\dfrac{12}{5}$