Answer:
1655
Step-by-step explanation:
Note the common difference d between consecutive terms of the sequence
d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3
This indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
Here a₁ = - 4, d = 3 and n = 90, thus
[tex]S_{90}[/tex] = [tex]\frac{90}{2}[/tex] [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655
