Answer:
-1875
Step-by-step explanation:
An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.
So our sequence so far looks like,
(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence
[tex]a _{1} + (n - 1)d [/tex]
where a1 is the inital value,
d is the common differnece and n is the nth term.
We need to find the nth term so
[tex]57 + (n - 1)( - 11) = - 207[/tex]
[tex](n - 1)( - 11) = - 264[/tex]
[tex]n - 1 = 24[/tex]
[tex]n = 25[/tex]
So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence
which is
[tex] \frac{a _{1} + a _{n} }{2} n[/tex]
[tex] \frac{57 + ( - 207)}{2} (25) = [/tex]
[tex] \frac{ - 150}{2} (25)[/tex]
[tex] - 75(25) = - 1875[/tex]
