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# The expressions for the sum to n terms of some arithmetic sequences are given below. Find the expression for the nth term of each:

2n^{2} – n

Answer :

S_{n} = 2n^{2} - n

a_{n + 1} = S_{n + 1} - S_{n}

= {2(n + 1)^{2}-(n + 1)}- {2n^{2} - n}

= (2n^{2} + 4n + 2-n-1)-(2n^{2}-n)

= 4n + 1

= 4(n + 1)-3

a_{n} = 4n-3

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Kerala Board Mathematics Part-1

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