Answer:
[tex]S_{45}[/tex] = 9000
Step-by-step explanation:
there is a common difference between consecutive terms , that is
11 - 2 = 20 - 11 = 9
this indicates the sequence is arithmetic with nth term
[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 = 2 and d = 9 , then
[tex]S_{45}[/tex] = [tex]\frac{45}{2}[/tex] [ (2 × 2) + (44 × 9) ]
= 22.5(4 + 396)
= 22.5 × 400
= 9000
