Concept: If a1,a2,...,an be an AP then Sn=a1+a2+...+an=‌
n
2
×(2a+(n−1)d) where a is the 1‌st ‌ term and d is the common difference. If a1,a2,...,an be an AP then the general term is given by: an=a+(n−1)×d where a is the 1‌st ‌ term and d is the common difference. Calculation: Here, we have to find the value of 1−2+3−4+5−+101⇒1−2+3−4+5−+101=(1+3+......+101)−(2+4+.....+100) As, we can see that (1,3,......,101) is an AP with a=1 and d=2. ⇒an=101=1+(n−1)×2⇒n=51 ⇒S51=1+3+...+101=‌
51
2
×(2+50×2)=2601 Similarly, (2,4,...,100) is an AP with a=2 and d=2 ⇒an=100=2+(n−1)×2 ⇒n=50 ⇒S50=2+4+...+100=‌