Answer:
4600
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = - 2 - (- 6) = 2 - (- 2) = 6 - 2 = 4
This indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 6 and d = 4 , then
[tex]S_{50}[/tex] = [tex]\frac{50}{2}[/tex] [ (2 × - 6) + (49 × 4) ]
= 25(- 12 + 196)
= 25 × 184
= 4600
