Question

Graph the first 10 terms of the arithmetic sequence an = 2 + 3n and the equation of the line y = 3x + 2. Compare the graphs and explain the differences.

Answer 1

There is no difference between the graphs of the arithmetic sequence and the equation of the line.

Explanation:

If we calculate the first 10 terms of the arithmetic sequence, putting n =1,2,3....,10

a1 = 5

a2= 8

a3= 11

a4= 14

a5= 17

..

a10= 32

The graph of arithmetic sequence is plotted by using term numbers and values of the terms.

And the points for equation will be calculated by putting x=1,2,3,...,10

x=1 , y = 5

x=2, y = 8

x=3, y = 11

..

..

x=10, y = 32

The first 10 terms for both arithmetic sequence and the points for line of equation are same.

So there will be no difference in graph..

Note: The attached graphs are sketched using the graph calculator at desmos.com

The red line graph is for arithmetic sequence and the blue one is for equation.