Find the sum of the following APs: (i) 2, 7, 12,..., to 10 terms. (ii) 37, 33, 29,..., to 12 terms. (iii) 0.6, 1.7, 2.8,..., to 100 terms. (iv) 115, 112, 110,...., to 11 terms.

(i)2,7,12..to10thtermHerea=2,n=10Andd=7−2;=5Sn=n2[2a+(n−1;)d]S10=102[2(2)+(10−1;)5]=5(4+9×5)=245(ii)37,33,29,to12thtermHerea=37,n=12Andd=33−37=−4Sn=n2[2a+(n−1;)d]S12=122[2(37)+(12−1;)(−4]=6(74−1;1×4)=−1;80(iii)0.6,1.7,2.8to100termHerea=0.6,n=100Andd=1.7−0.6=1.1Sn=n2[2a+(n−1;)d]S100=1002[2(0.6)+(100−1;)(1.1)]=50(1.2−99×1.1)=5505(iv)115,112,110...to11thterma=115,n=11d=112−1;15=5−460=160S11=112[2(115+(11−1;)160)]=112(215+1060)=112×930=3320