Question

If the sum of a certain number of terms of the AP 27,24,21,18,... Is -30,find the last term

Answer 1

D=-3 a=27 an=a+(n-1)d= 27-3n+3=nth term =30-3n Sn=n/2(a+nth term) -30=n/2(27+30-3n) -60=57n-3n^2 3n^2-57n-60=0 N^2-19n-20=0 N^2-20n+n-20=0 N(n-20) +1(n-20) (n+1)(n-20) So n is either-1 or 20,but n can't be -1 as it is the no. of digits. So n=20. -30= 20/2(27+nth term) 27+nth term=-3 Nth term=-30 Thus,the last term is -30