Answer:
2442
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d is the common difference
We require to find d knowing that 120 is the 44 th term, thus
[tex]a_{44}[/tex] = - 9 + 43d = 120 ( add 9 to both sides )
43d = 129 ( divide both sides by 43 )
d = 3
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], hence
[tex]S_{44}[/tex] = [tex]\frac{44}{2}[/tex] [ (2 × - 9 + (43 × 3) ]
= 22(- 18 + 129)
= 22 × 111 = 2442
OR
Since the first and last terms in the sequence are known, then
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last )
[tex]S_{44}[/tex] = 22(- 9 + 120) = 22 × 111 = 2442
