Question
Mathematics Question on limits and derivatives
The sum of n terms of an AP is n2 + n; the common difference will be:
A
(A) n - 1
B
(B) 1
C
(C) 2
D
(D) -4
Answer
(C) 2
Explanation
Solution
Explanation:
Sn=n2+n=n2[2a+(n−1)d]⇒a+(n−1)d2=n+1…(1)Again, Sn=n2+n∴Sn−1=(n−1)2+(n−1)∴Sn−Sn−1=n2+n−[(n−1)2+(n−1)]=n2+n−n2−1+2n−n+1or Tn=2n⇒a+(n−1)d=2n…(2)Subtracting(1) from (2), we get [n−1−(n−12)]d=2n−(n+1)Or d (n−12)=n−1∴d=2