Question

Describe the similarities and differences between arithmetic

sequences and linear functions.

Short answer

Similarities :

Few terms of Arithmetic sequence is same as linear functions

Both Arithmetic sequence and linear function increases by a constant.

Difference:

Arithmetic sequence is a discrete function . Linear function is a continuous function .

$$\begin{gathered} Arithmeticsequence \\ {a}_n=5x+7 \\ Linearfunctionislike \\ f\left(x\right)=5x+7 \end{gathered}$$

Step-by-step solution

Given Information 

Given arithmetic sequences and linear functions.

Similarities 

Few terms of Arithmetic sequence is same as some points on linear functions

Arithmetic sequence have constant difference. Linear function increases by a constant rate.

So, Both Arithmetic sequence and linear function increases by a constant.

Difference

Arithmetic sequence have few set of numbers. some gaps will occur.

the graph of Linear function is a continuous.

Arithmetic sequence is a discrete function . Linear function is a continuous function .

$$\begin{gathered} Arithmeticsequencewillbelike \\ {a}_n=5x+7 \\ Linearfunctionwillbelike \\ f\left(x\right)=5x+7 \end{gathered}$$