Answer:
The sum of the first 22 terms of the sequence is -1199.
Step-by-step explanation:
Arithmetic sequence:
The general term of a arithmetic sequence is given by:
[tex]A_n = a_1 + (n-1)r[/tex]
In which [tex]a_1[/tex] is the first term and r is the common difference.
The sum of the first n terms of a arithmetic sequence is given by:
[tex]S_n = \frac{n(a_1+a_n)}{2}[/tex]
First term is - 2 and the common difference is -5.
This means that [tex]a_1 = -2, a_n = -5[/tex]
Sum of the first 22 terms
[tex]S_{22} = \frac{22(-2+a_{22})}{2} = 11(-2+a_{22})[/tex]
In which
[tex]a_{22} = -2 + (22-1)(-5) = -107[/tex]
So
[tex]S_{22} = 11(-2 - 107) = 11(-109) = -1199[/tex]
The sum of the first 22 terms of the sequence is -1199.
