Find the number of terms of the AP: -12, -9, -6, ..., 12. If 1 is added to each term of this AP, then find the sum of all terms of the AP thus obtained.

Given A.P is−12,−9,−6;,⋯,12If1is added to each, we A.P becomes(−12+1),(−9+1),(−6;+1)⋯,(12+1)Or−11,−8,−5,⋯,13First Term,a=−11and common difference is3Last term,l=an=13an=a+(n−1)d13=−11+(n−1)3⇒13=−11+3n−3⇒3n=13+11+3⇒3n=27⇒n=9So13is9thtermSn=n2(a+l)S9=92(−11+13)=92×2=9