One of the basic and conceptual question from arithmetic progression chapter in which we have been asked to find the number of terms of the AP -12, -9, -6…….21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained.
Book – RS Aggarwal, Class 10, chapter 5C, question no 39.
l=a+(n−1)d
where l= last term
n=no. of terms
a=first term
21=−12+(n−1)3
21+12+3=3n−
36=3n
n=12
if 1 is added to each term then sequence become
−11,−8,−5,.....22
now
sn​=n/2​[a+l]
s12​=12/2​[−11+22]
s12​=6[11]
s12​=66