Answer :

Sn = n(4n + 1)


Sn - 1 = (n - 1)[ 4(n - 1) - 1]


= (n - 1)[ 4n - 5]


Sn - Sn - 1 = n(4n + 1) - (n - 1)(4n - 5)


(a1 + a2 + a3 + - - - + an - 1 + an) - (a1 + a2 + a3 + - - - + an - 1) = 4n2 + n - (4n2 - 5n - 4n + 5)


an = 11n - 5


For a1,


Put n = 1 so a1 = 11(1) - 5 = 6


For a2,


Put n = 2, so a1 = 11(2) - 5 = 17


For a1,


Put n = 3 so a1 = 11(3) - 5 = 28


For a1,


Put n = 4 so a1 = 11(4) - 5 = 39


So AP is 6, 17, 28, 39, …


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