Arithmetic sequence: a sequence where each term equals the previous term plus a common difference (d). Linear equation: y = mx + b, representing a straight line.
An arithmetic sequence is a series of numbers in which each term is obtained by adding a constant difference, denoted as 'd,' to the previous term.
The sequence is expressed as a, a + d, a + 2d, and so on, where 'a' represents the initial term.
This progression of values creates a linear pattern, revealing a constant rate of change.
In the context of linear equations, the second box illustrates the equation y = mx + b.
Here, 'y' is the dependent variable, 'x' is the independent variable, 'm' represents the slope, and 'b' is the y-intercept.
The slope, 'm,' signifies the rate of change, while the y-intercept, 'b,' is the point where the line intersects the y-axis.
The third box clarifies the mathematical interpretation of the linear equation.
It states that for any given 'x' value, the corresponding 'y' value can be determined by multiplying the slope 'm' by 'x' and adding the y-intercept 'b.'
This process embodies the concept of a constant rate of change, akin to the common difference in an arithmetic sequence, reinforcing the connection between arithmetic sequences and linear equations.