Question

Find the sum of AP 1.2.3..........to 20 terms​

Answer 1

Answer:

−4+9−16+25−.... to 2n terms

=(1−4)+(9−16)+(25−36)+.... to n terms. (after grouping)

=−3+(−7)+(−11)+....n terms

Now, the above series is in an A.P. with first term a=−3 and common difference d=−4

Therefore, the required sum =2n[2a+(n−1)d]

=2n[2(−3)+(n−1)(−4)]

=2n[−6−4n+4]=2n[−4n−2]

=2−2n(2n+1)=−n(2n+1).