If the sum of the series20+1935+1915+1845+… up to nth  term is 488 and the nth  term is negative, then :

The given sum is S=20+19+35+19+15+….n terms  The terms are in arithmetic progression with first term a=20, and the common difference d=-25 Hence, sum of first n terms is S=n2(2a+(n-1)d)Given 488=n2220+n−1−25=n20+1−n5=15100n+n−n2It gives n2−101n+5×488=0 Hence, n=40 (or) 61 Since the n th term is negative, tn=a+n−1d=20+61−1−25=20+60−25=20−24=−4 Therefore, n=61,tn=-4