Q6 of 50 Page 32

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

n2 + 2n

Sn = n2 + 2n


an + 1 = Sn + 1 - Sn


= {(n + 1)2 + 2(n + 1)}-{n2 + 2n}


= n2 + 4n + 4-n2-2n


= 2n + 4


= 2(n + 1) + 2


∴ an = 2n + 2


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