If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

an= a + (n–1) d = 2n + 1 (given)…………………(1)


Sn= n/2 (2a + (n–1) d)


By putting n=1 in (1)


a=3


similarly a2= 5


a3= 7


d= common difference = a2 – a1= 2


Sn = n/2 (6 + (n–1) 2)


= n/2(2n + 4)


= n (n + 2)

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