Unformatted text preview: is indeﬁnitely
greater than the power in the earth to produce subsistence for man. 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.” (See this webpage for more information.) Discuss this quote
with your classmates from a sequences point of view. 560 Sequences and the Binomial Theorem 7. This classic problem involving sequences shows the power of geometric sequences. Suppose
that a wealthy benefactor agrees to give you one penny today and then double the amount
she gives you each day for 30 days. So, for example, you get two pennies on the second day
and four pennies on the third day. How many pennies do you get on the 30th day? What is
the total dollar value of the gift you have received?
8. Research the terms ‘arithmetic mean’ and ‘geometric mean.’ With the help of your classmates,
show that a given term of a arithmetic sequence ak , k ≥ 2 is the arithmetic...
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