Question:

The sum of n terms of an AP is n2 + n; the common difference will be:

Updated On: Apr 27, 2024
  • (A) n - 1
  • (B) 1
  • (C) 2
  • (D) -4
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The Correct Option is C

Solution and Explanation

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

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