What are the similarities and differences between linear equations and arithmetic sequences?

Similarities:
Have a consistent change for every interval can be represented as functions of a variable points lie on a line.

Differences: linear equations represent all solutions to all x values, whereas arithmetic sequences pick integer spacing

Answer Link

yoodyannapolis yoodyannapolis · Answer 2 · 2021-10-04T11:29:40+02:00

Similarity is both have a constant rate of change.

Difference is that linear equation can have any values, the sequence have only specific values.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For example, starting with 2 and using a common difference of 3 we get the arithmetic sequence as:

2, 5, 8, 11, 14....

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one, two, three or more variables.

Now, the similarity would be that they both have a constant rate of change and the difference is that a linear equation can have any values, the sequence have only specific values.

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