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 – n

Sn = n2-n


an + 1 = Sn + 1-Sn


= {(n + 1)2-(n + 1)}-(n2–n)


= n2 + 2n + 1-n-1-n2 + n


= 2n


= 2(n + 1)-2


an = 2n-2


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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:

n2 – 2n

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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:

2n2 – n

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Calculate in head, the sums of the following arithmetic sequences.

i) 51 + 52 + 53 + … + 70


ii)


iii)

8

The sum of the first 10 terms of an arithmetic sequence is 350 and the sum of the first 5 terms is 100. Write the algebraic expression for the sequence.