Given sum of first n terms of an AP is 2n + 3n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is:

Given sum of n terms of AP is Sn=2n+3n2 For the first term substitute n=1 Hence, a1 = 5 The second term is a2=S2-S1=16-5=11 The common difference is a2-a1=11-5=6 Hence, the first term and common difference of the original sequence are a1 =5, d=6For the new sequnce, first term is same a=5 only  Common difference is two times of 6d=12Sum of first n terms of new AP is Sn=n22a+n-1dSn=n210+(n-1)12 =6nn-n =6n2-n