The Composition of Functions and Geometric Sequence - Assignment Example

The number ‘e’ in mathematics is an irrational number, which acts as the base for natural logarithms. In cases where the number ‘10’ acts as the base for common logarithms, e serves the same purpose for natural logarithms. In mathematical terms, where n tends to infinity, e is the limit. The approximation of e provided by Euler was up to eighteen decimal places. However, its numerical value goes beyond those eighteen decimal places.

Answer No: 3

The common aspect of arithmetic and geometric sequences is that there is always a common constant or ratio between any two consecutive terms of the sequences. For example, in the case of an arithmetic sequence, if the constant of difference between a term and its preceding term is 4, it will be 4 for the whole sequence. Similarly, in the case of a geometric sequence, if the ratio of the difference between a term and its preceding term is 2, it will be 2 for the whole sequence.

The difference between arithmetic and geometric sequences is that in an arithmetic sequence, a specific constant is a difference between any term and its preceding term. On the other hand, in the case of a geometric sequence, there is always a specific ratio between any term and its preceding term.