Answer
4400
Work Step by Step
The given series = -10, -6, -2, 2
Common difference d = 2 - (-2) = (-2) - (-6) = (-6) - (-10) = 4
$1^{st}$ term ($a_{1}$) = -10
To solve this type question, first find the $50^{th}$ term, after that find the sum.
$50^{th}$ term = $a_{1}$ + (50 - 1) d
= -10 + 49 $\times$4
= -10 + 196
= 186
Sum of all terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 50 terms of given sequence = $\frac{50}{2}$(-10 + 186)
= $\frac{50}{2}$(176)
= 25$\times$176
= 4400
