Sequences and series

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Sequences and series

Population, when unchecked, increases in a geometrical ratio.

Subsistence increases only in an arithmetical ratio. a slight

acquaintance with numbers will show the immensity of the first

power in comparison with the second.

ThomasMalthus(1798)

●?^ Each of the following sequences is related to one of the pictures above.

(i) 5000, 10 000, 20 000, 40 000, ....

(ii) 8, 0, 10, 10, 10, 10, 12, 8, 0, ....

(iii) 5, 3.5, 0, –3.5, –5, –3.5, 0, 3.5, 5, 3.5, ....

(iv) 20, 40, 60, 80, 100, ....

(a) Identify which sequence goes with which picture.

(b) Give the next few numbers in each sequence.

(c) Describe the pattern of the numbers in each case.

(d) Decide whether the sequence will go on for ever, or come to a stop.

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