Given sum of the first n terns of an AP is $$2n$$ $$+$$ $$3$$ $$n2$$. 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

Question

Given  sum of  the  first n terns  of an  AP  is  $$2n$$ $$+$$ $$3$$ $$n2$$. 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

Infinity Learn · Accepted Answer

Here,$$T1=S1=2(1)+3(1)2=5T2=S2$$−$$S1=16$$−$$5=11$$∵$$S2=2(2)+3(2)2=16T3=S3$$−$$S2=33$$−$$16=17$$ ∵$$S3=2(3)+3(3)2=33Hence$$, sequence is $$5$$, $$11$$ , $$17$$.∴ $$a=5$$ and $$d=6For$$ new AP,$$A=5$$,$$D=2$$×$$6=12$$∴ Sn′$$=n2$$[$$2$$×$$5+(n$$−$$1)12$$]$$=6n2$$−n

Given sum of the first n terns of an AP is 2n + 3 n². 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

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Given sum of the first n terns of an AP is 2n + 3 n2. 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

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Given sum of the first n terns of an AP is 2n + 3 n². 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