ANSWER
-1026
EXPLANATION
The sum of the first n terms in an arithmetic sequence is,
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]As we can see, we have to find the nth term of the sequence,
[tex]a_n=a_1+(n-1)d[/tex]In this case, the first term is 9 and the common difference is -7 - note that each term is the previous one minus 7. So the formula for the nth term is,
[tex]a_n=9-7(n-1)[/tex]We have to find the 19th term,
[tex]a_{19}=9-7(19-1)=9-7\cdot18=9-126=-117[/tex]So the sum of the first 19 terms is,
[tex]S_{19}=\frac{19\cdot(9+(-117))}{2}=\frac{19\cdot(9-117)}{2}=\frac{19\cdot(-108)}{2}=\frac{-2052}{2}=-1026[/tex]Hence, the sum of the first 19 terms of the given sequence is -1026.
