등차수열 합

등차수열 $\left\{ a _{n} \right\}$의 첫째항을 $a ,$ 공차를 $d$라 하면 $a _{1} + a _{10}$$= a + ( a + 9 d )$ $= 2 a + 9 d = 22$ 이므로 $\displaystyle \sum\limits _{k = 2} ^{9} a _{k}$$= a _{2} + a _{3} + \cdots + a _{9}$ $\displaystyle = \frac{8 ( a _{2} + a _{9} )}{2}$ $\displaystyle = \frac{8 ( a + d + a + 8 d )}{2}$ $= 4 ( 2 a + 9 d )$ $= 4 \times 22 = 88$