Answer
Sum of first 100 terms $S_{100}$ = -29,300
Work Step by Step
The given sequence = 4, -2, -8, -14....................
This is a arithmetic sequence so the sum find by formula
$S_{n}$ = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
In the given sequence first term $a_{1}$ = 4
Common difference (d) = -6
Sum of first 100 terms $S_{100}$ = $\frac{100}{2}$($a_{1}$ + $a_{100}$)
$a_{100}$ = 4 + (100 - 1)(-6) = 4 - 594 = -590
$S_{100}$ = $\frac{100}{2}$(4 - 590) = 50 $\times$ -586 = -29,300
