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Answer:
See explanation below
Step-by-step explanation:
<u>1. Arithmetic Sequence and Linear Functions</u>
An arithmetic sequence is defined as a sequence of numbers one that has a constant difference, also called common difference, between two adjacent terms. Therefore the rate of change in an arithmetic sequence is the same roughout the sequence.
<em>Example</em>: The sequence 2, 4, 6, 8, 10,.... is an arithmetic sequence where the common difference is 2
A linear function has a constant rate of change (slope). In that manner, both arithmetic sequences and linear functions are similar
However, while an arithmetic sequence is composed of discrete values, a linear function is continuous and can be described in the form of an equation y= mx + c where m is the slope(rate of change) and c the y value where the function intersects the y axis(i.e. x = 0)
<em>Example: </em>y = 2x + 2 is the equation of a linear function which has +2 slope and passes through the point (0,2) on the y axis
<u>1. Geometric Sequence and Exponential Functions</u>
A geometric sequence is a sequence of numbers where there is a common ratio between any two adjacent numbers. So to find the next number in a geometric sequence, multiply the previous number by the common ratio
For example, the following is a geometric sequence where the common ratio is 2
2, 4, 8, 16, 32, 64, 128, ...., .....
As you can see the numbers rise more rapidly as the sequence goes on. This type of grown is also called exponential growth. An exponential function also has a common ratio except that the function is continuous compared with a geometric sequence which has discrete values
For example, y = 2ˣ is an exponential function that doubles its value with every x value and is continuous (see graph below)
