ANSWER
[tex]S_{30}= - 3390[/tex]
EXPLANATION
The given sequence is
3,-5,-13,.....-229.
The first term of this sequence is
a_1=3
There is a common difference of
[tex]d = - 5 - 3 = - 8[/tex]
The last term of this sequence is -229.
The nth term of this sequence is given by:
[tex]a_n=a_1+d(n-1)[/tex]
We use the last term to determine the number of terms in the sequence.
[tex] - 229 = 3 + - 8(n - 1)[/tex]
[tex]- 229 - 3= - 8(n - 1)[/tex]
[tex]- 232= - 8(n - 1)[/tex]
Divide through by -8;
[tex]29= (n - 1)[/tex]
[tex]n = 30[/tex]
Hence there are thirty terms in the sequence.
The sum of the first n terms is given by:
[tex]S_n= \frac{n}{2} ( a_{1} + l)[/tex]
The sum of the first 30 terms is given by:
[tex]S_{30}= \frac{30}{2} ( 3 + - 229)[/tex]
[tex]S_{30}=15( - 226)[/tex]
[tex]S_{30}= - 3390[/tex]
