Find the sums given below: (i) 7 + 10 + 13 + ... + 84 (ii) 34 + 32 + 30 + ... + 10 (iii) -5 + (-8) + (-11) + ... + (-230)

(i)7,1012,1484Here, firsta=7andl=84d=1012−7=312=72an=a+(n−1;)d84=7+(n−1;)72⇒84−7=72(n−1;)⇒n−1;=22⇒n=23and last terml=84We know thatSn=n2(a+l)Sn=232(7+84)=23×912=20932=104612(ii)34,32,3010Herea=34,l=10d=32−34=−2;an=a+(n−1;)d10=34+(n−1;)(−2;)⇒10−34=(−2;)(n−1;)⇒n−1;=12⇒n=13and last terml=10We know thatSn=n2(a+l)Sn=132(34+10)=13×442=286(iii)−5+(−8)+(−1;1)+...+(−2;30)Herea=−5,l=−2;30d=(−8−(−5))=−3an=a+(n−1;)d230=−5+(n−1;)(−3)⇒−2;30+5=(−3)(n−1;)⇒n−1;=75⇒n=76and last terml=−2;30We know thatSn=n2(a+l)Sn=762(−5+(−2;30)=−8930