Answer
$S_{30}= -330$
Work Step by Step
Given sequence $a_{n} = 18 + (n-1)(-2)$
It is in the form of arithmetic sequence $a_{n} =a_{1}+ (n-1)d$
$a_{1} = 18 + (1-1)(-2)$
$a_{1} = 18 $
$a_{30} = 18 + (30-1)(-2)$
$a_{30} = 18 + (29)(-2)$
$a_{30} = 18 - 58$
$a_{30} = -40$
Partial sum of arithmetic sequence $S_{n} = \frac{n}{2}(a_{1}+a_{n})$
Substituting $n=30$
$S_{30} = \frac{30}{2}(a_{1}+a_{30})$
Substituting $a_{1} ,a_{30}$ values
$S_{30} = 15(18-40)$
$S_{30} = 15(-22)$
$S_{30}= -330$
