Explanation Similarities and differences between geometric sequences and exponential functions. Geometric Sequences Exponential functions To get to the next term in a geometric sequence you multiply the last term in the sequence by the common ratio An exponential function is multiplied by the same factor every time the independent value is increased by one unit A geometric sequence is discrete An exponential function is continuous Discrete means that the sequence has values only at distinct points (the 1st term, 2nd term, etc) Continuous means that the function has values for all possible values of x . The integers are included, but also all the numbers in between. We use a geometric series to describe quantities that have values at discrete points We use exponential functions to describe quantities that have values that change continuously Here are two examples one discrete and one continuous. Discrete sequence: An ant walks past several stacks of Lego inlines. There is one inline in the first stack, 3 inlines in the 2nd stack and 9 inlines in the 3rd stack. In fact, in each successive stack there are triple the number of inlines than there were in the previous stack...

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 12.3, Problem 112AYU

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Chapter 12.3, Problem 111AYU

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Chapter 12 Solutions

EBK PRECALCULUS

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The similarities and differences between geometric sequences and exponential functions with example.

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