Given, arithmetic sequence 57, 54, 51, ....., k. Here first term a=57, Difference d=-3, Last term=k, Sum of all terms=-123
Sum of the n terms of an A.P. = (n/2)[2a + (n-1)d]
-123 = (n/2)[2*57 + (n-1)*(-3)]
⇒ n² - 39n - 82 = 0
(n-41)(n+2) = 0
Considering positive value of number of terms, n=41 ⇒ k=41th term of the series.
Now, n th term of an AP = a + (n-1)d
.'. k = 57 + 40*(-3) = -63