The sum of the first terms of a sequence is given by

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The sum SnS_n of the first nn terms of a sequence is given by Sn=4n2−nS_n = 4n^{2} - n. (i) Show that the sequence formed by the individual terms is an arithmetic progression. (ii) Find the first term and the common difference. (iii) Determine the sum of the first 30 terms. (iv) Which term of the sequence equals 283?

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