Question

Explain how the common difference in an arithmetic sequence is like the slope of a linear function. read more >>

Answer 1

In arithmetic sequence, let the first tern of the arithmetic sequence be, a, and the common difference, d, then the nth term, Tn, of the arithmetic sequence is given by:


`T_n=a+(n-1)d`

For a linear function with y-intercept, c, and slope, m, the linear function is given by:


`y=mx+c`

Comparing the equation of the arithmetic sequence and that of the linear function, we can see that y is compared to Tn, a is compared to c, m is compared to d, and x is compared to n - 1.

Therefore, the common difference in an arithmetic sequence is like the slope of a linear function as both are multiple of a variable.