Two sequences are given below: A: B:

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Two sequences are given below: A: 5,  9,  13,  17,…5,\;9,\;13,\;17,\ldots B: 2,  −6,  18,  −54,…2,\;-6,\;18,\;-54,\ldots (i) For each sequence, identify whether it is an arithmetic progression or a geometric progression. (ii) For sequence B, determine the constant quantity (common difference or common ratio, as appropriate) and show all working that justifies your conclusion. (iii) Explain briefly why checking the constancy of the ratio an+1an\dfrac{a_{n+1}}{a_n} is a decisive test for recognising a geometric progression.

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